Bayern had been poised to sign Palhinha in 2023 and the defensive midfielder had even posed in the club's strip for promotional pictures, but the transfer from Premier League club Fulham fell through.
At his official unveiling as a Bayern player on Tuesday, Palhinha said he "didn't think Bayern would come back for me".
"When the transfer didn't happen, it was a disappointment for me and my family. It was a hard one to digest," added the Portuguese.
Palhinha signed a contract extension with Fulham just a month after the transfer failed in September 2023, but sealed his move to Bayern earlier in July this year.
"The first impressions have been really great. It's a dream come true and I can't wait to put the shirt on and represent Bayern on the pitch," he said.
The 29-year-old, who spent two years at Fulham after arriving from Sporting Lisbon in 2022, signed a four-year contract with the Bavarians.
Palhinha, who has scored twice in 31 international appearances, took part in Portugal's Euro 2024 campaign which ended at the hands of France in the quarter-finals.
"I'm a Bayern player. I'm ready to play," said Bayern's new number 16.
Bayern sporting director Max Eberl said Tuesday: "Last year it just didn't work out. For Joao it was really dramatic, but for the club it wasn't too nice either. Now we were able to get it done."
Eberl also said that the club would not change their summer transfer strategy despite an injury to defender Hiroki Ito on Sunday.
Summer arrival Ito broke a bone in his foot and is likely to miss eight to 10 weeks.
The sporting director said the injury "is bad and unlucky, but it doesn't change our approach".
"It's simply bad luck," Eberl said, adding "the squad can't become too big."
