Sharp was working alongside Rangnick at Lokomotiv Moscow before the German left to take up the role as interim manager at Old Trafford.
Sharp joins Chris Armas, who was appointed assistant coach earlier this month, and the pair have previously worked together at New York Red Bulls and Toronto FC.
Sharp came into the professional game through the US college system, spending two years as director of performance analysis at Northwestern University.
Sports psychologist Sascha Lense has also been recruited as United prepare to return to action following the postponement of their matches against Brentford and Brighton as a result of a coronavirus outbreak.
First-team training resumed at Carrington on Tuesday with a staggered return for the players ahead of their clash with Newcastle on December 27.
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