The Galaxy sent Angel across the hallway at Home Depot Center for a third-round pick in next year's supplemental draft.
Los Angeles agreed to terms on Monday with Keane, the Irish national team captain and Tottenham Hotspur striker. Keane will join the Galaxy this week, and he's expected to make his MLS debut Saturday against the San Jose Earthquakes.
The Galaxy had to clear a spot for Keane among its three "designated players" who can be paid above the MLS salary cap. Landon Donovan and David Beckham aren't going anywhere, so Angel was moved after one disappointing season in Los Angeles.
Angel was MLS' leading scorer over the previous four seasons, but the Colombian forward had just three goals and one assist in 22 games after joining the Galaxy in the offseason.
Angel will be expected to provide an offensive boost to Chivas USA, which is fighting to stay in the MLS playoff race. The Goats began the week in sixth place in the Western Conference standings with 30 points.
Although the Galaxy lead the overall MLS standings with 48 points in their bid for a second straight Supporters' Shield, they've struggled with inconsistent goal-scoring from their forwards, most notably Angel. Donovan is second in MLS with 11 goals while lining up largely at midfield, but no other Los Angeles player has more than four goals.
The 31-year-old Keane is the 10th-leading goal-scorer in Premier League history, but he fell out of favor in Tottenham and welcomed a move to MLS.
Donovan scored as Los Angeles beat Honduran club Motagua 2-0 on Tuesday night in the opener of CONCACAF Champions League group play.