The Portugal midfielder arrives from Fulham for a fee rising to €50m.
Bayern's sporting director, Christopher Freund, said: "We have held firm since last summer, and now we finally have João Palhinha with us. He will be very valuable to FC Bayern. João is strong in tackles and very good in the air.
"He can give the team structure and continuously plays mature football. He also has a strong character and is a true leader. Bayern fans can look forward to seeing João Palhinha."
Max Eberl, who sits on the sports board, is also satisfied.
"João Palhinha was highly sought after by FC Bayern last summer – and with good reason. It was important that we never lost contact. João really wanted to go to Bayern and we need that kind of player. He is an important building block for the future.
"He has once again proven his strength on the biggest stage at the EC, and he brings a lot of experience, having previously played both the EC and the WC and appeared around 300 times in the Portuguese and English leagues.
"He will give us greater stability in midfield. "
Bayern have a deal with Palhinha until the summer of 2028.