He will succeed Ole Gunnar Solskjaer, who left the club this month, and after his initial six-month spell in charge, the German will take on a consultancy role with the club for two further years.
But what attracted United to Rangnick and vice versa? What kind of manager is he? Is he likely to be a success and what will his role beyond this season entail?
And what will his appointment mean for Cristiano Ronaldo?
To answer these questions, the BBC spoke to St. Louis SC sporting director Lutz Pfannenstiel, who worked with Rangnick at Hoffenheim, former Leicester defender Christian Fuchs – who played under him at Schalke – and European football journalists Raphael Honigstein, Guillem Balague and Julien Laurens.