It was announced on Tuesday that the Borussia Dortmund star is set to join die Roten in the summer for €37.5 million and the current Switzerland coach revealed his frustration that the switch did not happen sooner.
"I was irritated that Bayern did not sign him last year or the year before that, when you could see that Gotze is one of the biggest talents in German football. Bayern has made a lot of money and I think they acquired Gotze for a reasonable price,” he told the Bundesliga’s official website.
"Of course the news did surprise me. But the fact that Gotze would join Bayern one day, that was no secret, I guess. It is a logical consequence in his development."
The former Bayern coach, who won five Bundesliga titles and a Champions League trophy with the club, added that he does not think that Gotze will reach Lionel Messi’s level but Pep Guardiola will help him improve regardless.
"When he plays in an even stronger team, his strengths might even be more obvious. Can he can match Messi at some point? I don't think so. Messi sets the standards.
"He is not only very good at assisting but he scores an incredible amount of goals, too. To be as good as Messi he needs some more years of education. But, with Pep Guardiola, he will move in the right direction."
Hitzfeld is worried about the effect the move could have on one of his national team members, Xherdan Shaqiri, and thinks some players will have to leave the club this summer to accommodate incoming transfers.
"Guardiola is a coach who pays attention to players who are technically strong," he added. "He likes these players and he gives them a chance in his system.
"That is why I hope Xherdan Shaqiri will have his breakthrough at Bayern. It will be more difficult now though now that Gotze is coming.
"This might hint of some players to be sold in the summer. To have too many very strong players can lead to frustration, especially if the success is missing."