The German playmaker will join Bayern next season.
The attacking midfielder’s release clause in his contract has been activated by Bayern, according to his agent Volker Struth, and his club, Dortmund, and he will join the German champions on July 1.
The fee is reportedly set at €37m (£31.5m).
Dortmund confirmed the transfer on their Facebook page early on Tuesday, although the club stressed at the time that they had yet to hear anything official from the newly-crowned Bundesliga champions.
The statement read: “Mario Götze’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.”
Hans-Joachim Watzke, Borussia Dortmund’s CEO, also stated: “We are obviously disappointed beyond measure, but emphasise that both Mario and his advisers have behaved within the terms of the contract. From Bayern Munich there has been nothing official on this matter up to this date.”
Bayern later made an official announcement, on their website, saying, “Bayern Munich confirm that the club have reached an agreement with national team player, Mario Götze, 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 Götze.”
The club added that they had wanted to wait until after Dortmund’s Champions League semi-final meeting with Real Madrid on Wednesday before making them aware, in an attempt not to distract them from the match.
Dortmund have asked for fans to support Götze and the rest of the players as they seek a place in the Wembley final against Bayern or Barcelona.
Their statement continued: “Coach Jurgen Klopp and sporting director Michael Zorc asks all fans of Borussia Dortmund to support Mario Götze 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.”
Losing Götze, especially to their closest domestic rivals, will be a huge blow to Dortmund who recently lost the Bundesliga title they won in the past two seasons to Bayern.
With this move, Gotze will become the most expensive German player of all time. The 20-year-old has emerged as one of the most coveted players in European football since coming through the ranks at Dortmund and making his Bundesliga debut in November 2009. He has been courted by other top European clubs, including Arsenal.
He played a key role for Dortmund as they won back-to-back Bundesliga crowns and has made 22 appearances for Germany, scoring five goals.
The only factor limiting his dominance in the playmaker role for Germany is the presence of Real Madrid’s Mesut Ozil, a player more favoured by the German coach for that position.
In January, Bayern announced former Barcelona coach Pep Guardiola will succeed Jupp Heynckes as boss this summer, having signed a three-year deal.
It is not clear the role played by Pep in the signing of Gotze, but he will be the first player signed by Bayern since Pep’s announced arrival.