Apocalypse's history seemingly mirrors that of his Earth-1610 counterpart up to a certain point. Utilizing the powers of mutants he forcibly stole, Apocalypse quickly began taking over the world, starting with New York City. The X-Men attempted to stop him, but Apocalypse killed Charles Xavier and stole his powers, along with those of Wolverine, whom he grievously injured in the attempt, removing his left arm and right eye.
Exactly what happened in the immediate aftermath of that is unknown, but eventually Apocalypse managed to conquer the world, with only a few mutants, such as Bishop and the Six Pack fighting against him.
Eventually, Wolverine, now going by the name Cable, found a way to travel back in time to prevent Apocalypse from taking over the world.