The 18-year-old has signed a three-year deal at the Reebok Stadium, and makes the move only two weeks after bagging a hat-trick against Bolton in a pre-season friendly.
Eaves came through the ranks at Oldham, and quickly caught the eye of several clubs.
Manager Owen Coyle said: "We're delighted to have him and we'll look to gradually take step upon step with him, to such a time where he is ready to challenge for a first-team place.
"The fact he played in that pre-season game and did very well against us just cemented what we already knew about him, and that is that he is a young player with great potential making his way in the game.
"We'd been and watched him previous to that. He played against Liverpool four days earlier and did very well. So we were very much aware of him before our friendly at Boundary Park, and we had actually started dialogue with Oldham before that match."
Eaves is the fifth summer signing for Bolton, following Martin Petrov, Robbie Blake, Marcos Alonso and Ivan Klasnic.
However, he may be the last to actually feature for Coyle's senior squad.
"He's not the finished article, he's got a lot to improve on, but he's committed to work hard and do that," Coyle added.
"What he does have is a lot of attributes that we're looking to bring into the football club.
"He's 6ft 4in, he's mobile, he works his socks off and has an eye for goal as well.
"So for a young player, making his way up, he has an opportunity and we'll provide him a platform."