Is a game really "on Steam" if launching it through Steam launches another launcher, namely EA's Origin? It's debatable, but for the sake of simplicity, I'll say that Apex Legends is coming to Steam this fall.
EA is in the process of bringing all of its games to Steam, actually, and earlier today it added The Sims 4, Titanfall 2, and a few others (opens in new tab).
Apex Legends is probably the most complicated EA game to make the leap, given its living nature. Adding to the job for Respawn, the developer also announced that Apex Legends is getting crossplay support, which will cover Origin, Steam, Xbox One, PS4, and a new Switch version. How Respawn will manage the keyboard and mouse vs controller problem is unknown right now.
Like the Steam release, crossplay is cheduled to arrive in the fall.