Rangnick will pen a three-year deal with Milan, becoming the third person to coach the fabled club since Gennaro Gattuso departed in May 2019.
The 62-year-old German is set to replace Stefano Pioli and will reportedly hold discussions with the 18-time Italian champions over the possibility of becoming the club's technical director, a post currently held by team legend Paolo Maldini.
Maldini will reportedly be offered a role as a club ambassador, which he's expected to reject.
Rangnick is a well-traveled manager in German football. He won the DFB-Pokal Cup with Schalke before rising to prominence with RB Leipzig after performing sporting director duties for both the Bundesliga outfit and sister club Red Bull Salzburg.
Since leaving Leipzig at the culmination of the 2018-19 campaign, Rangnick worked as the head of sport and development soccer for the Red Bull energy drink company's football holdings.