Sharp worked alongside Rangnick at Lokomotiv Moscow, though he first encountered the coach during his spell at New York Red Bulls.
It was with Toronto FC that Sharp made his name as a performance analyst and Rangnick has moved quickly to appoint the coach following the departures of Michael Carrick and Kieran McKenna.
Sharp joins the club with Chris Armas, who he worked alongside in Canada.
McKenna left United last week to take the manager’s role at Ipswich and it means Mike Phelan is the only remaining first team coach from the set-up under Ole Gunnar Solskjaer, with Darren Fletcher’s role still unclear.
Rangnick is well known for his man-to-man management and he wants his coaches to be equally hands-on with the first team squad.
The German has a clear philosophy and though he’s only set to be in charge for the remainder of the season, United want to appoint a successor to Solskjaer in Rangnick’s image.