The 61-year-old has long been linked with a move to the San Siro, but there were doubts over what role he would take within the Rossoneri hierarchy.
Sport Mediaset reports the German will step down from his post as head of football operations with Red Bull in the next 10 days before holding talks with Milan chief Gordon Singer.
All the finer points of the agreement have reportedly been finalized, with the report suggesting Rangnick will sign a three-year contract with an option for a fourth that will pay him €5 million a season.
It’s believed the German will take over as coach and sporting director, giving him final say in recruiting players as well.
An announcement isn’t expected until August at the earliest, with the likes of Stefano Pioli, Ricky Massara and Paolo Maldini all expected to make way in what is expected to be a major overhaul at the San Siro.