Van Nistelrooy was appointed interim head coach of the 20-time English champions after Erik ten Hag was sacked at the end of last month, with the Dutchman losing his job off the back of the 2-1 defeat at West Ham United on October 27.
The club's former striker took charge of four games, and he went unbeaten, with two of those wins coming over Leicester, while he also guided the Red Devils to a 2-0 success over PAOK in the Europa League.
Van Nistelrooy also oversaw a 1-1 draw with Chelsea in the Premier League, and it will go down as a successful spell for the Dutchman, but he has now moved aside for Amorim, who has arrived from Sporting Lisbon.
Amorim closed his time at Sporting on Sunday evening with a 4-2 win over Braga in Portugal's top flight, with the team coming from two goals behind to triumph in an incredible finish, and he will next be in a dug-out when Man United travel to Ipswich Town in the Premier League on November 24.
Sporting will be devastated by his departure, but he has left the club in incredible shape, having overseen 11 league wins from 11 matches this season, while the club are second in the overall Champions League table, picking up 10 points from their four games, including a 4-1 success over Manchester City.
Does Amorim have a visa?
At this moment, Amorim, who has signed a contract at Old Trafford until June 2027, is yet to receive his visa, meaning that he is currently unable to conduct training sessions at Man United despite travelling to Manchester to begin work at his new club.
However, according to the Manchester Evening News, the visa will be 'processed quickly', allowing him to 'get on the grass'.
The delay is not particularly problematic due to the November international break, as there will not be a full team training session until the players have returned from international duty, with a number, as expected, called up by their countries.
Marcus Rashford, Casemiro, Amad Diallo, Mason Mount and Antony are among those who will be immediately available for training sessions, while fit-again duo Leny Yoro and Luke Shaw should also be involved in his first sessions.
Which Man United players will be involved for their countries in November?
Diogo Dalot, Bruno Fernandes, Lisandro Martinez, Alejandro Garnacho, Christian Eriksen, Rasmus Hojlund, Matthijs de Ligt, Joshua Zirkzee, Noussair Mazraoui, Victor Lindelof, Manuel Ugarte, Andre Onana and Altay Bayindir are the first-teamers who will feature for their national teams during the international break.
Man United have players travelling to represent Uruguay and Argentina, and Amorim may not have the squad back together until the latter stages of the week before the clash with Ipswich on November 24, so his preparation for his first game in charge will not be ideal.
Amorim will be able to settle into his new environment at a slower pace, though, which is a major benefit of him arriving at this stage of the season.
According to the Daily Mail, Amorim wants to bring five of his backroom staff at Sporting with him to Old Trafford, although there has not yet been confirmation over the identify of those, while Van Nistelrooy's future remains unclear.
Man United's injury problems are easing at the perfect time
The only players not to have been in training with Man United over the last week are Harry Maguire, Kobbie Mainoo and Toby Collyer, with all three players still on the sidelines.
Mainoo is now close to making his return, though, while Tyrell Malacia, Yoro and Shaw are now taking part in full sessions, with Man United receiving a huge triple injury boost heading towards the festive period.
Antony, Mount and Eriksen have also recently recovered from injury problems in time for Amorim's arrival, so the Portuguese is set to have a strong squad available for the clash with Ipswich after the international break.
Amorim will be hoping that all of his players get through their national team fixtures unscathed, but the returns of Yoro, Mainoo and Shaw could be particularly crucial for the new head coach.
A new era has officially begun at Old Trafford, and Amorim has arrived with a glowing reputation, winning five trophies at Sporting, including two league titles, and he has set the Green and Whites up to enjoy more success during the current season, with his ability to impact matches again on full display in Sporting's stunning win over Braga on Sunday night.