"Dante has certainly been one of our best transfers in the past few years," said chief executive Karl-Heinz Rummenigge in a statement. "He has developed into one of our key players on and off the pitch."
The 30-year-old earned his first Brazil call-up last year and is hoping to win a World Cup place on home soil in June.
Bayern, who meet Manchester United in the Champions League quarter-finals next month, will clinch the Bundesliga title on Tuesday if they win at Hertha Berlin.
(Reporting by Karolos Grohmann; editing by Tony Jimenez)
