But Old Trafford fans will wonder why the Belgian was United's only big acquisition while Arsene Wenger splashed out a club record fee, believed to be £43m, to bring German international Mesut Ozil to Arsenal.
Moyes paid £27.5m to prise the 25-year-old Fellaini from Everton - after chaotic and, at times, shambolic deadline-day dealing.
A decision to let a clause in Fellaini's contract expire at the end of July backfired as it ended up costing United an additional £4m, turning him into the fourth most expensive purchase in the Red Devils' history.
However, having worked with Fellaini for five years at Goodison Park, Moyes is aware of the former Standard Liege man's qualities.
He said: "Marouane is not someone you want to be playing against. He has attributes other people don't have. I am sure he will be a big player for Manchester United."
The Scot - who took over from Sir Alex Ferguson in July - will be relieved to bolster his midfield options. With Paul Scholes retired and Darren Fletcher no nearer making a comeback from a chronic bowel condition, United desperately needed reinforcements and Fellaini provides a variety of options.
"He can play higher up the field if we need him to, just behind a main striker," said Moyes.
"He can play as a defensive or holding midfield player. In fact he is comfortable in any position in the middle of the field.
"It was definitely a position where people would say we were short. I am glad we have got him."
United failed in a late move for Real Madrid left-back Fabio Coentrao after a bid to sign England full-back Leighton Baines was rejected by Everton.Ozil said he decided to join Arsenal when it became clear he no longer figured in the first-team plans of Madrid manager Carlo Ancelotti following the world-record signing of Gareth Bale from Tottenham
The 24-year-old German World Cup player has no doubts he can take his game to a whole new level at the Emirates Stadium to repay the faith of manager Arsene Wenger.
He said: "I was certain I would stay at Real Madrid, but I realised I did not have the faith from the coach or the bosses. I am a player who needs this faith and that is what I have felt from Arsenal, which is why I have joined.
"Wenger gives me the faith and I can develop further. I know what I can do and I know that I could make the grade with any club in the world."
The news of Ozil's departure caught his former Real Madrid team-mates unawares.
Defender Sergio Ramos said: "If it was up to me he would be one of the last players to go. But he and the club have made their decision and I can only wish him the best. He's a unique player and it's a shame."
Madrid playmaker Isco, who joined from Malaga this summer, said: "It has surprised me. Ozil has a lot of quality and is a player who is capable of changing a game."
Alvaro Arbeloa said: "It's a big loss to the dressing room. He's very different, there's no player like him in the world. He makes the difference on the pitch."