The Colombia international will spend two years, at least, at Allianz Arena, with the Bundesliga side holding the option to buy him outright
James Rodriguez has signed for Bayern Munich on a two-year loan from Real Madrid.
The Colombia international, 25, has been linked with a move away from the Champions League winners since the start of the summer.
Manchester United were reported to be keen on James but Bayern have swooped in to secure his services until June 2019.
The Bundesliga club have confirmed that they have the option to purchase James outright once his loan deal ends.