Bayern confirmed Hummel's departure to AFP subsidiary SID on Wednesday afternoon, after German magazine Kicker reported that Dortmund had signed Hummels on a three-year deal for an estimated fee of €38 million ($43.6m).
The 30-year-old defender twice won the Bundesliga title with Dortmund before joining Bayern for 35 million euros in 2016.
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He has since made 118 appearances for Bayern in the last three years, winning three Bundesliga titles and the domestic double in 2019.
After Arjen Robben, Franck Ribery and Rafinha, Hummels is the latest senior player to leave Bayern in 2019.
Despite solid performances in 2018/19, Hummels' future in Munich was thrown into doubt after Bayern made two high-profile defensive signings as part of their major squad overhaul ahead of next season.
The Munich giants signed Lucas Hernandez for a club record 80 million euros, as well as fellow French World Cup winner Benjamin Pavard for 35 million euros.
Dortmund, meanwhile, have been on the lookout for an experienced defender after nervy performances at the back cost them crucial points in a nail-biting Bundesliga title race last season.
Dortmund also appeared to confirm the transfer on Twitter, posting an emoji of a bumble bee, the German word for which is "Hummel".
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