Angel, who played in England's Premier League with Aston Villa, spent the past four seasons with the New York Red Bulls, scoring an impressive 58 goals in 102 regular season games.
Angel joins Beckham and Donovan under the 'designated player rule' which allows clubs to pay selected players largely outside of the salary cap limit.
"He has been one of the best goalscorers in MLS over the last four years and I fully expect that he will be a productive and consistent player in a Galaxy uniform."
Angel, 35, represented the Colombia national team on 33 occasions scoring nine goals.
(Reporting by Simon Evans in Miami; Editing by Julian Linden)