The midfielder played under Ten Hag at Utrecht at the start of his career and was determined to link back up with him at United as he wrapped up a long-discussed deal at the start of September.
Asked if it was a difficult process waiting to get the move, Amrabat said: “Yes, of course.
“After the last game with the club, it was the Conference League final with West Ham and from that moment, the window started for me.
“A lot of clubs, a lot of speaking, talking, but for me it was clear I wanted Manchester United.
“It was long, long months for me, difficult months for me, but at the end it’s nice on the last day that I signed here and that I’m here is now the most important (thing).”
United paid 10million euros (£8.6m) to sign Amrabat on loan for the season, with the deal including the option to trigger a permanent move.
The Serie A will receive a 20m euros (£17.1m) fee and up to 5m euros (£4.3m) in potential add-ons if that option is taken by Ten Hag’s men.
“I don’t think about that,” Amrabat said of his future beyond this season. “For me, today, I am a Manchester United player.
“The only thing I can do is every day to give everything that I have, to do my best, to try to help the team.
“I hope we have a fantastic season, I hope we can win something and then later we will see what will happen.
“Of course, I would love to stay here, but that’s not important for me. I don’t look too far into the future.”
Amrabat spoke as he basked in the afterglow of an impressive first appearance at Old Trafford, where he helped United beat Crystal Palace 3-0 in the Carabao Cup third round.
“It was fantastic,” he said with a smile. “It was a dream of mine. Since I was a child I worked for this every day and to be here is a dream, it’s fantastic.”
After a small injury delayed his debut, Amrabat finally made his bow off the bench in Saturday’s much-needed win at Burnley before making his first start against Palace three days later.