The defender, who left Dortmund for Bayern in 2016, will head back to the Westfalenstadion for a reported €38 million (£33.8million).
Bayern said in a statement they had “agreed to a deal for the transfer of the centre-back”, who will now undergo a medical at Dortmund.
The 30-year-old, who won the Bundesliga title in each of his three seasons at the Allianz Arena, is returning to the club he first joined from Bayern in 2009, winning two league titles in his first spell there.
He established himself as one of most highly regarded defenders in Europe in his seven years at Dortmund and was a key member of the Germany team which won the World Cup in 2014.
Hummels has won 70 caps, but his international career is on hold in the wake of the team’s awful 2018 World Cup and Nations League campaigns.
Boss Joachim Low has opted to focus on the next generation of German players, with Hummels one of the old guard who has been told he is not in the coach’s plans.
Know more about Sport360 Application