Palhinha, who moved to Fulham in 2022, made 79 appearances for the Premier League club in all competitions, while he has also featured 31 times for Portugal's senior team.
While financial details were not disclosed, The Athletic reported the deal was worth 51 million euros.
"This is one of the happiest days of my life. I'm now playing for one of the top clubs in Europe," Palhinha said in a statement.
Palhinha had been close to joining Bayern in 2023 but the transfer fell through on deadline day.
"Joao Palhinha was highly sought after by Bayern even last summer – and rightly so," Bayern board member for sport Max Eberl said in a statement.
"It was important that we never lost touch. Joao really wanted to come to Bayern, and we need players like that. He’s an important building block for our future."
Bayern Munich appointed Vincent Kompany as coach after their 11-year reign as Bundesliga champions was ended by Bayer Leverkusen.
Palhinha is Bayern's second major signing of the close season window to come from the Premier League following their acquisition of winger Michael Olise from Crystal Palace.
