Alonso will be Bayern's fifth Spanish player along with Pepe Reina, Juan Bernat, Thiago Alcantara and Javi Martinez.
The deal comes shortly after the club signed central defender Mehdi Benatia from AS Roma for a reported €25 million.
Alonso, 32, retired from international football on Wednesday and within hours was linked with the Bundesliga champions.
"This is purely sporting decision because Alonso can instantly help us and boost our quality," Bayern sports director Matthias Sammer said. "He can play top level football for at least two more years."
Real were happy to let Alonso leave for the club managed by former Barca boss Pep Guardiola, with Bayern reportedly giving the Spaniard an annual salary of €10 million.

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Xabi Alonso joins Bayern Munich
German Club, Bayern Munich has signed Real Madrid Midfielflder, Xabi Alonso for an estimated €10 million deal.
32-year old Alonso only retired recently from international football.
The deal comes shortly after the club signed central defender Mehdi Benatia from AS Roma for a reported €25 million.
The former Spain international has to his credit, winning in the World Cup, two European Championships, two Champions Leagues and the Liga title – has made 236 appearances for Real Madrid, who he joined from Liverpool in 2009.
www.tv360nigeria.com/xabi-alonso-joins-bayern-munich

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