Guardiola left the Nou Camp in the summer, but having taken a sabbatical he will return to management in Germany next summer.
His former assistant Tito Vilanova, now in charge of Barcelona, backed the move.
"I am very happy that he is returning to football," he said. "I did not know where he was going as there was a confidentiality agreement.
"I do not know how many teams or what kind of contracts he was offered, but I am sure they were all top level. He has had time to think about where to go.
"Bayern are an historic club. They have four Champions League titles to their name, and their facilities are fantastic."
Carles Puyol, the Barcelona captain, added his support for the man who won three Liga titles and the Champions League twice during his tenure.
"They [Bayern] are a very good team, and he's a fantastic manager,” the Spaniard said. “He is going to one of the big clubs in Europe.”
“It was expected for him to manage a great club, and that is what Bayern is," Javier Mascherano said. "They have a lot of German players, they have a defined philosophy and style of play."