The attacker was loaned to Juve in the close-season for €6m with the Serie A side holding an option to buy him for a further €40m.
Costa is yet to break into the first-team at the Turin giants, having started just five of his 10 Serie A appearances.
However, the reigning Italian champions will spend the full fee to take him on a permanent deal at the end of the campaign, as Bayern CEO Rummenigge confirmed at the club’s annual general meeting.
“Douglas Costa joined Juventus on loan last summer,” he said. “At the same time he will definitively join Juventus next summer for €46m overall.”
Bayern have taken a six-point lead at the top of the Bundesliga after reappointing Jupp Heynckes as Carlo Ancelotti’s successor.
Although the Italian was sacked early in the season, Rummenigge took time to thank him for his work at the club.
“I want to thank Carlo Ancelotti. He is a good person and a very good coach,” he said. “We became German champions together, but sometimes a successful coach and a successful club do not fit together.
“The decision to sack him so early in the season was not easy, but professionally necessary. When I told him the decision, Carlo said: ‘Okay, you are not my boss anymore, but you stay my friend.’ That’s something which is rare. I wish him and his team all the best.”