Bayern, who face Real Madrid in the Champions League semi-finals next week and Kaiserslautern in the German Cup last four on Wednesday, are looking for a second consecutive treble of titles this season.
"I am very happy that the transfer worked out," the 23-year-old Rode, who is coming back from a month-long absence due to a right knee injury, said in a statement.
"Bayern is the next big step in my career. I want to further develop here and win a bunch of titles," added Rode, who still hopes to play for Frankfurt in some of the remaining games this season.
(Reporting by Karolos Grohmann, editing by Pritha Sarkar)