The 27-year-old, who joined on loan from Fiorentina on deadline day, came through Utrecht’s academy to play 50 times for the senior side during Ten Hag’s spell in charge between 2015 and 2017.
“It was very important because I was very young,” he told the club’s website.
“I was 18, 19 years old and he gave me the chance to play in the first team with Utrecht.
“We had a fantastic time, a really good season. I learned a lot from him so maybe he’s one of the most important people in my career for now.
“It’s fantastic because I think Erik ten Hag is a coach who will push always to the limit.
“He’s hungry. He wants to win. He’s a winner and I like that. I think I’m also similar, I’m also a winner. I want to win every day so it’s a good match.”
Amrabat, one of the best players of the winter World Cup in Qatar for Morocco, has been brought in to bolster United’s midfield.
United have paid an £8.6million loan fee but have an option to make the deal permanent for £17.1m plus £4.2m in add-ons.
His brother, Nordin, previously played for Watford in the top flight and he is looking forward to following in the footsteps of some famous United midfielders.
“I think United had so many fantastic players and young midfielders,” he added.
“So, in general, I look more to the midfielders like Paul Scholes, Roy Keane, David Beckham.
“But there were so many big players. Gary Neville, Rio Ferdinand, Louis Saha, Wayne Rooney, (Cristiano) Ronaldo. I can go on for one hour to say names.
“Of course, (my brother and I) spoke about it. He told me that he thinks that I have to go to the Premier League, it is the strongest league in the world so now I’m here, I can’t wait.”