The 24-year-old will move to Munich on a free transfer from next season with a four-year contract until 2018. (Agencies)
"I am very happy that the transfer worked out. Bayern are the next big step for me," Rode said.
Munich sports director Matthias Sammer rated Rode as "an excellent professional" who "will give the team a lot of drive to master upcoming tasks".
After wrapping up the Bundesliga title in record time with seven games to spare, Bayern also stormed into the semifinals of Champions League as they overpowered English champions Manchester United 4-2 over two legs in the quarterfinals.
However, they lost 3-0 at their home turf this weekend against bitter rivals Borussia Dortmund, who had lost to Spanis giants Real Madrid over two legs in the Champions League quarterfinal stage.
The 24-year-old will move to Munich on a free transfer from next season with a four-year contract until 2018.