Van Nistelrooy maintained his unbeaten record during his four-match stint in charge, securing a convincing 3-0 victory against Leicester on Sunday.
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The former PSV Eindhoven boss, appointed as an assistant coach in July, had said he wanted to stay at Old Trafford to work with Amorim, who arrived at the club's Carrington training complex on Monday afternoon.
But United issued a brief statement on Twitter confirming Van Nistelrooy, 48, would not be part of the new coaching set-up.
"Ruud van Nistelrooy and three first-team coaches have departed the club with our best wishes for the future," it said. "Thank you for your unwavering commitment to United."
Ruud ❤️#MUFC pic.twitter.com/n4wXc1a75t
— Manchester United (@ManUtd) November 11, 2024×Van Nistelrooy, who scored 150 goals during a stellar playing career for United, said after overseeing his third win in four games in all competitions that he had enjoyed his time at the helm.
"I really enjoyed it, it's been a short but amazing period," he said. "We are in an uncertain position but we tried to do our jobs and help the club, which is important.
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 Ipswich on November 24, following the current international break.
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