"We're extremely pleased and happy to bringing one of the most talented German internationals to FC Bayern and we're convinced that Podolski will be a perfect fit to our future philosophy," Bayern chairman Karl-Heinz Rumminege told the club's website.
Podolski still had a year left in his contract with Cologne but his 12 goals for the club this season were not enough to keep them in the Bundesliga and the player expressed his desire to leave in order to secure a place in a first-division club next season.
"I'm delighted it's all worked out, I'm looking forward to Munich, the city and the club, Bayern are the undisputed number one," Podolski told the club's official website.
"I had a great time at Cologne, but I've always said that another season at the second division wouldn’t have been right for me," Podolski added.
Podolski will be leading Germany's front line alongside Miroslav Klose in the World Cup and it is reported that Bayern paid around 10 million Euros for the 20-year-old striker who was also chased by both Werder Bremen and Hamburg.
"I've also considered offers from Werder and Hamburg but I wanted to test myself against the best, now I can finally focus with the German team," Podolski said.
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