The Orioles will get back minor league right-handers Isaac Mattson, Zach Peek, Kyle Bradish and Kyle Brnovich as part of the deal, sources told ESPN.
Bundy was once a prized prospect of the Orioles, who made him the fourth overall pick in the 2011 draft. He went 10-6 with a 4.02 ERA in 2016, his first full season in the Baltimore rotation, striking out 104 in 109.2 innings.
But the right-hander has struggled of late, losing 16 games with a 5.45 ERA in 2018, and then going 7-14 with a 4.79 ERA this past season.
The Angels are hoping Bundy can turn things around out west. He will join a rotation that is expected to include a fully healthy Shohei Ohtani and could add free-agent Gerrit Cole or Stephen Strasburg, whom the Angels reportedly have interest in.
Bundy has a 7.64 ERA in four games (three starts) at Angel Stadium, his fourth-worst ERA of any ballpark (minimum three starts), according to ESPN Stats & Information research.
The Athletic first reported the agreement between the sides.