The 28-year-old Austrian key man left the Bundesliga champions following the end of the 2020-21 campaign and has joined the Galaticos.
Los blancos have confirmed the signing of utility man David Alaba on a free transfer following the expiration of his contract at Bayern Munich.
Real confirmed that Alaba has signed a five-year deal at the club and will join up with his new team-mates after the European Championships, at which Alaba will be a key figure in the Austrian side.
Alaba arrives at Real as one of the most decorated an experience individual footballers in Europe, having won 28 different titles after joining Bayern in 2008.
These include two Champions League titles, and 10 successive Bundesliga crowns.He played 431 games for Bayern – a record for a non-German footballer – scoring 33 goals, and was named in UEFA Team of the Year three times.