"I have agreed a deal with Cologne starting from July 1, 2009," the 23-year-old striker said on his personal website.
"I am glad the decision for my future has been taken and all speculation about me is finally over." Cologne said the deal was for four years.
No financial details of the deal were released but Podolski will reportedly cost Cologne 10 million euros, roughly the same fee Bayern paid for him in 2006.
Podolski, who has been a very successful striker for the national team scoring 31 goals in 60 appearances, could not find a regular starting spot at Bayern since signing for the champions.
The recent addition of striker Landon Donovan, on loan from the Los Angeles Galaxy, and the signing of Hamburg's Ivica Olic who will boost the Bayern attack from next season, had made matters worse for Podolski.
He already had to compete with established strikers Miroslav Klose and Luca Toni.
"I have had very good discussions with (Cologne coach) Christoph Daum and (Cologne manager) Michael Meier and I am fully convinced of the club's concept. I look forward to this challenge," he added.
Cologne chairman Wolfgang Overath said he was delighted the player had chosen Cologne.
"I am glad Lukas is returning to us. He followed his heart," Overath told the club website.
"I am also delighted that we as a newly promoted club could sign a Germany international like Lukas Podolski."
Eleventh-placed Cologne, relegated in 2006 and promoted last year, are in need of goals, having scored only 19 times in 17 matches in the league. The Bundesliga season resumes in just under two weeks.
The Polish-born striker, voted the best young player at the 2006 World Cup in Germany, is adored in Cologne, where he played from his youth until switching to Bayern in a much-hyped move.
