Dortmund revealed the news on their Facebook page, although they were keen to stress they had yet to hear anything official from Bayern.
"Mario Gotze's agent Volker Struth told us a few days ago that the player wishes to make use of his release clause and on July 1, 2013 move to Bayern Munich," read the Dortmund statement.
Dortmund chief executive Hans-Joachim Watzke admitted he would be sorry to see Gotze go but admitted the player had not broken his contract to secure the move.
"We are obviously disappointed beyond measure, but emphasise that both Mario and his advisers have behaved within the terms of the contract," he said.
"From Bayern Munich there has been nothing official on this matter up to this date."
Bayern subsequently released a statement confirming the deal which read: "Bayern Munich confirm that the club have reached an agreement with national team player Mario Gotze that he will play for Bayern Munich from 1 July 2013.
"Bayern are prepared to meet the release clause agreed between Borussia Dortmund and Mario Gotze."
The timing of the announcement is unhelpful for Dortmund, who face Real Madrid at the Westfalenstadion in the first leg of their Champions League semi-final on Wednesday.
Dortmund have urged fans to get behind Gotze and the rest of the team though, as they look to secure a place in the Wembley final against Bayern or Barcelona.
The statement added: "Coach Jurgen Klopp and sporting director Michael Zorc ask all fans of Borussia Dortmund to support Mario Gotze unconditionally as they would any other player in the final games of the season, but especially in the important Champions League semi-final against Real Madrid."
Klopp's side recently lost the Bundesliga crown they won in each of the past two seasons, with Bayern claiming the title in record time.