The Dutchman, a former star striker at the club, was appointed as interim manager following the sacking of Erik ten Hag 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 over the weekend.
The former PSV Eindhoven boss, appointed as an assistant coach 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,” they 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.
“We are grateful for his contribution and the way in which he has approached his role throughout his time with the club. He will always be very welcome at Old Trafford.”
United also said fellow coaches Rene Hake, Jelle ten Rouwelaar and Pieter Morel had also left the club.
“We will confirm the full men’s first-team coaching composition in due course,” they added.
Van Nistelrooy, who scored 150 goals for United, said he had relished his time in charge.
“I really enjoyed it, it’s been a short but amazing period,” he said after the Leicester win. “We are in an uncertain position but we tried to do our jobs and help the club, which is important.
“There are a lot of feelings there, the way the fans supported me and the team always in difficult moments... To close down this block of games with good results and a good connection I can’t thank them enough.”
Amorim was named as the new United boss earlier in November.
The 39-year-old jetted to Britain from Portugal on Nov 11 after completing his stint as Sporting Lisbon boss with a 4-2 win against Braga.
He was met at the club’s Carrington training complex by chief executive Omar Berrada, and was also welcomed by sporting director Dan Ashworth and technical director Jason Wilcox.
The former Portugal international is United’s sixth permanent appointment since the end of Alex Ferguson’s trophy-filled 27-year-reign in 2013.
United are 13th in the Premier League table after a poor start to the season but are only four points off the top four.
Amorim’s first match in charge will be away at struggling Ipswich on Nov 24, following the current international break.
In other news, Premier League referee David Coote was suspended by the PGMOL referees’ body pending a full investigation after a video circulated on social media showing the official allegedly abusing Liverpool and former manager Jurgen Klopp.
The video allegedly shows Coote making derogatory comments about Klopp, who left Anfield in May.
The video has not been verified by Reuters, it is unclear when it was filmed or its authenticity.
“David Coote has been suspended with immediate effect pending a full investigation. PGMOL will be making no further comment until that process is complete,” PGMOL said. AFP,