Van Nistelrooy sent a special message to Manchester United and their fans after Amorim's arrival to the club.
Van Nistelrooy who led the team temporarily after the sacking of ten Hag helped United to win three games and have a draw. They also defeated Leicester City twice.
Van Nistelrooy posted on Instagram: "To everyone at Manchester United football club, in particular the backroom staff, the players and the fans.
"I want to thank you from the bottom of my heart for your incredible efforts and support. It has been a privilege and honour to represent the club as a player, coach and manager, and I will always cherish the memories we have shared together.
"M.U.F.C will always have a special place in my heart, and I hope there are many more glory days at Old Trafford very soon - not only because I want the club to do well, but because you all deserve it!"
Amorim's first game as a head coach of the Red Devils will be a Premier League game against Ipswich Town next week.