Amor fati is a Latin phrase, but the doctrine it names is older. The phrase itself is most famously associated with Nietzsche, who gave a Latin label to a doctrine the Stoics had taught — it is his coinage, not a Stoic survival. He gave it back to modern readers in Ecce Homo: 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.
The Stoic version is more disciplined and less ecstatic than Nietzsche's. Marcus Aurelius articulates it across the Meditations — at 4.23 (Everything harmonizes with me, which is harmonious to thee, O Universe), at 10.21 (I say then to the universe, that I love as thou lovest), and at 10.6 (the cosmic-providence framing). The move is not Stoic resignation to fate (which is bad practice — it implies grudge held in silence). It is Stoic endorsement of fate — actively willing what the universe has brought, as if you had chosen it.
The distinction matters. The dichotomy of control teaches you to stop expending effort on what is not yours. Amor fati asks for more: not just to release your grip on what is outside your power, but to want it as it is. The Stoic heimarmenē — fate as the rational order of the cosmos — is what is being endorsed; the prohairesis is what does the endorsing. This is harder. It is also where Stoic practice becomes a kind of religion in the philosophical sense — not theistic religion, but a fundamental orientation toward existence that has a positive content, not just a negative discipline.
In practice, the test of amor fati is what you do with the next genuine setback. The mere accepter says: this is happening; I will not waste energy resisting it. The Stoic in amor fati says: this is happening, and it is part of the whole, and the whole is what I will to be — so this too is what I will. The second posture is harder to manufacture and impossible to fake. But where it is genuine, even disasters lose their power to derail.
Marcus Aurelius, Meditations 4.23, 10.6, 10.21