The Dutchman, a former star striker at the club, was put in temporary charge after Erik ten Hag was sacked in October.
He oversaw three wins and a draw in his four-match spell, signing off with a 3-0 victory against Leicester City in the Premier League on Nov 10.
The former PSV Eindhoven boss, appointed as an assistant manager in July on a two-year contract, had voiced a desire to stay at Old Trafford to work with Amorim.
But United issued a statement confirming the 48-year-old would not be part of the new coaching set-up.
"Manchester United can confirm that Ruud van Nistelrooy has left the club," it said. "Ruud rejoined in the summer and has taken charge of the team for the past four matches as interim head coach. Ruud is, and always will be, a Manchester United legend.
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