Mortality was given to the Atani as a gift "which as Time wears even the Powers shall envy." (S.48) The evidence for this comes from the following: the words of Ilúvatar, the Númenorean customs relating to death, the Elves warning to Númenor, Gandalf's words about the One Ring, the choice of Lúthien, and the choice given to the Peredhil.

Mortality was given as a gift as proven by the following quotes of the words of Ilúvatar and the Valar referring to his decisions. " 'But to the Atani I will give a new gift.' Therefore he willed that the hearts of Men should seek beyond the world and should find no rest therein" (S.47). This is the gift of Mortality, which has also been seen as a grief by Men who fell under the dominion of Morgoth and those who envied the life of the Eldar. "For it was not permitted to the Valar to withhold Death from him, which was the gift of Ilúvatar to Men." (S.225) At death, the Atani leave the Circles of the World forever. Where they go, only Mandos and Manwë, even of the Valar know. "Death is their fate, the gift of Ilúvatar, which as Time wears even the Powers shall envy." (S.48)

The customs relating to death for the Atani uncorrupted by Morgoth were for the Man in question to lay down his or her life when he or she felt it was time. "But Bëor at the last had relinquished his life willingly and passed into peace." (S.179) This custom held true for the Númenoreans until the middle of the Second Age of the Sun, when they began to envy the Eldar and the Valar, longing for unending life. For the Númenorean Kings, this time was usually around their fourth century, until the waning of their wisdom and the increase of their pride. The first of the Númenorean Kings to break this custom was Tar Atanamir, "for he was the first of the Kings to refuse to lay down his life, or to renounce the sceptre; and he lived until death took him perforce in dotage." (UT.221) It seems that in the time of the Exiles, meaning the realms of Arnor and Gondor, this tradition was no longer followed, and in fact, no longer something the Atani could do except as a special gift.
"Nay, lady, I am the last of the Númenoreans and the latest King of the Elder Days; and to me has been given not only a span thrice that of Men of Middle-Earth, but also the grace to go at my will and give back the gift." (RK.424-425)
By the time of the Third Age only Aragorn and those of the Peredhil that had chosen the fate of the Atani were known to have been given this gift.

As the Númenoreans grew more proud and became envious of the life of the Eldar, they began to talk against the Ban and to long for everlasting life, like that of the Eldar. "For the Elves die not till the world dies, unless they are slain or waste in grief (and to both these seeming deaths they are subject); neither does age subdue their strength, unless one grow weary of ten thousand centuries; and dying they are gathered to the halls of Mandos in Valinor, whence they may in time return." (S.48) The twenty-fifth King of Númenor, Ar-Pharazôn, sent a fleet to Middle-Earth, to conquer the armies of Sauron. In fact, the might of the Númenorean armies were so great that the hosts of Sauron fled, and Sauron had to use guile to effect the downfall of Númenor. So he humbled himself to the King and was taken back to Númenor as a prisoner. However, Sauron soon became the chief councilor and Ar-Pharazôn began to persecute the Faithful even more than before, including sacrificing them to Morgoth in hopes of eternal life.
"But for all this Death did not depart from the land, rather it came sooner and more often, and in many dreadful guises. For whereas aforetime men had grown slowly old, and had lain them down in the end to sleep, when they were weary at last of the world, now madness and sickness assailed them; and yet they were afraid to die and go out into the dark and the realm of the lord they had taken". (S.329)

As this pride grew and the Númenoreans became more prideful and envious of the Eldar and the Valar, they were sent warnings of what might be to come. These messages were first sent in the time of Tar-Atanamir.
"But this we hold to be true, that your home is not here, neither in the Land of Aman nor anywhere within the Circles of the World. And the Doom of Men, that they should depart, was at first a gift of Ilúvatar. It became a grief to them only because coming under the shadow of Morgoth it seemed to them that they were surrounded by a great darkness." (S.318)
For Death was given as a gift to the Atani, but if they do not give back their lives when it is time they were given this warning. "And the Valar bid you earnestly not to withhold the trust to which you are called, lest soon it become again a bond by which you are constrained." (S.318) We envied the Eldar, because unless slain, they live as long as the Earth shall last, and they envy us because we are not tied to the Circles of the World for good or ill, and when we die we leave it forever.

Each of the Eruhíni is given a span of years, which it cannot naturally go over. For Hobbits, this is around a century. For the Dúnedain near the end of the Third Age of the Sun, between a hundred and a hundred and fifty years, (Aragorn was an exception to this, living until he was a hundred and ninety and giving up his life freely) and for the rest of the Atani, around a century. The Quendi live as long as the Earth shall exist, unless slain by weapons or by grief. The life-span for one of the Khazâd was around two and a half centuries, but they were made to have a long life. The Great Rings could stretch this time, but they had many negative effects, most of which were caused by Sauron and the One Ring.
"A mortal, Frodo, who keeps one of the Great Rings does not die, but he does not grow or obtain more life, he merely continues, until at last every minute is a weariness." (FR.72)
The reason for this was because the longer a bearer of one of the Great Rings held onto it, the more he was "stretched" past his normal life-span. "Of course it is a poor sort of long life that the Ring gives, a kind of stretched life rather than a continued growing - a sort of thinning and thinning."(VI.79) A good example of this would be Bilbo, or even more so, Gollum, who had the One Ring for nearly six centuries. Gollum no longer possessed the Ring, rather it possessed him, for he was completely bound to it. Bilbo certainly noticed the stretching effect of the Ring, for he told Gandalf: "Why, I feel all thin, sort of stretched, if you know what I mean: like butter that has been scraped over too much bread." (FR.55) At that time he did not know the Ring was the cause. The belief of an allotted life-span is shown in the following quotes: "But your kinsman possessed this thing longer than you. He is ancient in years now, according to his kind;" (RK.304) and "the view is taken … that each 'Kind' has a natural span integral to its biological and spiritual nature." (L.131note)

The choice of Lúthien Tinúviel was a special exception, made only because of the high doom of her descendants. Lúthien had followed Beren in death, when he had died from wounds incurred in the quest of the Silmaril.
"These were the choices he gave to Lúthien. Because of her labours and her sorrow, she should be released from Mandos, and go to Valimar, there to dwell until the world's end among the Valar, forgetting all griefs that her life had known. Thither Beren could not come. For it was not permitted to the Valar to withhold Death from him, which is the gift of Ilúvatar to Men. But the other choice was this: that she might return to Middle-Earth, and take with her Beren, there to dwell again, but without certitude of life of joy. Then she would become mortal, and subject to a second death, even as he; and ere long she would leave the world for ever and her beauty become only a memory in song." (S.225)
Lúthien chose mortality, as told in the Lord of the Rings, and from her marriage to Beren came the Half-Elven, who had a large part to play in the fate of the World. Of the Peredhil came, Elros, who was the first King of Númenor and Elrond who played a major part in the events of the Third Age. From the line of Elros came the Kings of the Realms in Exile, Arnor and Gondor. Of that line was Aragorn, the first King of the Reunited Kingdom. It was in part, his work distracting Sauron, which allowed the destruction of the Ring and the victory of the West over the Dark Lord and the forces of Mordor.

Arwen Undómiel made the same choice, which for her was the one of the choices given to the Half-Elven, as she said to Frodo at their parting. "I shall not go with him now when he departs to the Havens; for mine is the choice of Lúthien, and as she so have I chosen, both the sweet and the bitter." (RK.306) The sweet, because she loved Aragorn and was now wed to him, and the bitter, because she would never see her father or her mother again for they had gone to the Havens before, and also because as one of the Peredhil, she had long life, even with this choice. Elros Tar-Minyatur lived for five centuries four-hundred and ten of which he was the first King of Númenor, before laying down his life. Arwen laid down her life the year after Aragorn died, though of his own free will, in the Fourth Age, year 121. In their parting she gained more understanding of the Gift of Ilúvatar. Even with her knowledge, she pled with him to wait before making this choice for "she was not yet weary of her days, and thus she tasted the bitterness of the mortality that she had taken upon her" (RK.424).
"Would you then, lord, before your time leave your people that live by your word?" she said.
"Not before my time," he answered. "For if I will not go now, then I must go soon perforce. And Eldarion our son is a man full-ripe for kingship." (RK.424)

The Gift of Men was also called the Doom of Men, for as Arwen said in her final parting from Aragorn:
"There is now no ship that would bear me hence, and I must indeed abide the Doom of Men, whether I will or I nill: the loss and the silence. But I say to you, King of the Númenoreans, not till now have I understood the tale of your people and their fall. As wicked fools I scorned them, but I pity them at last. For if this is indeed, as the Eldar say, the gift of the One to Men, it is bitter to receive." (RK.425)
The gift of Ilúvatar later gained this name, for to most of the Atani, death was not a gift, rather it was a doom, to be put off as long as long as possible, so that instead of dying of free will, they died of old age as Aragorn said. "Take counsel with yourself, beloved, and ask whether you would indeed have me wait until I wither and fall from my high seat unmanned and witless." (RK.424)

Given the choice of the Peredhil who chose Mortality, sometimes called "the choice of Lúthien", the words of Ilúvatar, the evidence of the Rings of Power, and of the warnings given to the Númenoreans, Mortality was given to the Atani as a gift. As proved above, Mortality was given as a gift "that even the Powers shall envy" (S.48) Death is the fate of the Atani, to leave the Circles of the World forever.