The club gave no financial details.
Hummels will become the third key Dortmund player since 2013 to switch to Bayern, after Germany team mate Mario Goetze and Poland striker Robert Lewandowski.
"After long and intense deliberations Mats Hummels has decided to return to his hometown of Munich after eight-and-a-half years at BVB," club CEO Hans-Joachim Watzke said in a statement.
Hummels, a 27-year-old central defender who played over 200 games for Dortmund, has 46 international caps for Germany and was in the side that won the 2014 World Cup in Brazil.
He won the 2011 and 2012 Bundesliga with Dortmund as well as the 2012 German Cup. He also reached the 2013 Champions League final with the Ruhr valley club.
"I was and still am proud to wear the Borussia shirt and be part of this exceptional team," Hummels said.
"Before returning in the summer to my hometown we have a big goal and that is to bring the German Cup back to Dortmund and celebrate with a big football party."
Dortmund are second in Germany's Bundesliga, with Bayern already crowned champions and the teams meet in the Cup final on May 21.
(Reporting by John Stonestreet and Karolos Grohmann, editing by Ed Osmond)
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