The concept of amor fati has been linked to Epictetus. It has also been linked to the writings of Marcus Aurelius, who did not himself use the words (he wrote in Greek, not Latin).
The phrase is used repeatedly in Friedrich Nietzsche's writings and is representative of the general outlook on life that he articulates in section 276 of The Gay Science:
I want to learn more and more to see as beautiful what is necessary in things; then I shall be one of those who make things beautiful. Amor fati: let that be my love henceforth! I do not want to wage war against what is ugly. I do not want to accuse; I do not even want to accuse those who accuse. Looking away shall be my only negation. And all in all and on the whole: some day I wish to be only a Yes-sayer.
It is important to note that Nietzsche in this context refers to the "Yes-sayer", not in a political or social sense, but as a person who is capable of uncompromising acceptance of reality per se.
Quotation from "Why I Am So Clever" in Ecce Homo, section 10:
My formula for greatness in a human being is amor fati: that one wants nothing to be different, not forward, not backward, not in all eternity. Not merely bear what is necessary, still less conceal it—all idealism is mendacity in the face of what is necessary—but love it.