A £27.5 million deadline day capture from Everton, Fellaini is the first central midfielder to join the champions since Owen Hargreaves in 2007.
The Belgian was also his manager's most expensive acquisition at Everton and Moyes lauded the midfielder's versatility.
Open Image Modal
Moyes brought Fellaini to England five years ago
"Fellaini can do several different jobs, score goals and is effective in different areas," the Scot said at a press conference on Friday. "I hope he can continue to improve.
"We've got a busy schedule and I wanted to play a different way in different games. Marouane Fellaini helps me to do that.
"Fellaini's presence is very noticeable for many reasons, including his size. But you can't overlook his technical ability."
Fellaini unveiled
Soccer - Barclays Premier League - Manchester United Press Conference - Marouane Fellaini Unveiling - Old Trafford(01 of10)
Open Image Modal
New Manchester United signing Marouane Fellaini during a photocall at Old Trafford, Manchester. (credit:PA)
Soccer - Barclays Premier League - Manchester United Press Conference - Marouane Fellaini Unveiling - Old Trafford(02 of10)
Open Image Modal
New Manchester United signing Marouane Fellaini during a photocall at Old Trafford, Manchester. (credit:PA)
FBL-ENG-PR-MAN UTD-FELLAINI(03 of10)
Open Image Modal
Manchester United's newly signed Belgian midfielder Marouane Fellaini (L) poses during a photocall with Manchester United's Scottish manager David Moyes at Old Trafford in Manchester, north-west England on September 13, 2013. Fellaini became Moyes first United signing for a fee of 27.5 million GBP (32.7 million Euros). AFP PHOTO/ANDREW YATES RESTRICTED TO EDITORIAL USE. No use with unauthorized audio, video, data, fixture lists, club/league logos or live services. Online in-match use limited to 45 images, no video emulation. No use in betting, games or single club/league/player publications. (Photo credit should read ANDREW YATES/AFP/Getty Images) (credit:Getty Images)
FBL-ENG-PR-MAN UTD-FELLAINI(04 of10)
Open Image Modal
Manchester United's newly signed Belgian midfielder Marouane Fellaini (L) poses during a photocall with Manchester United's Scottish manager David Moyes at Old Trafford in Manchester, north-west England on September 13, 2013. Fellaini became Moyes first United signing for a fee of 27.5 million GBP (32.7 million Euros). AFP PHOTO/ANDREW YATES RESTRICTED TO EDITORIAL USE. No use with unauthorized audio, video, data, fixture lists, club/league logos or live services. Online in-match use limited to 45 images, no video emulation. No use in betting, games or single club/league/player publications. (Photo credit should read ANDREW YATES/AFP/Getty Images) (credit:Getty Images)
FBL-ENG-PR-MAN UTD-FELLAINI(05 of10)
Open Image Modal
Manchester United's newly signed Belgian midfielder Marouane Fellaini (L) poses during a photocall with Manchester United's Scottish manager David Moyes at Old Trafford in Manchester, north-west England on September 13, 2013. Fellaini became Moyes first United signing for a fee of 27.5 million GBP (32.7 million Euros). AFP PHOTO/ANDREW YATES RESTRICTED TO EDITORIAL USE. No use with unauthorized audio, video, data, fixture lists, club/league logos or live services. Online in-match use limited to 45 images, no video emulation. No use in betting, games or single club/league/player publications. (Photo credit should read ANDREW YATES/AFP/Getty Images) (credit:Getty Images)
Soccer - Barclays Premier League - Manchester United Press Conference - Marouane Fellaini Unveiling - Old Trafford(06 of10)
Open Image Modal
New Manchester United signing Marouane Fellaini and manager David Moyes during a photocall at Old Trafford, Manchester. (credit:PA)
Soccer - Barclays Premier League - Manchester United Press Conference - Marouane Fellaini Unveiling - Old Trafford(07 of10)
Open Image Modal
New Manchester United signing Marouane Fellaini during a photocall at Old Trafford, Manchester. (credit:PA)
Soccer - Barclays Premier League - Manchester United Press Conference - Marouane Fellaini Unveiling - Old Trafford(08 of10)
Open Image Modal
New Manchester United signing Marouane Fellaini and manager David Moyes during a photocall at Old Trafford, Manchester. (credit:PA)
Soccer - Barclays Premier League - Manchester United Press Conference - Marouane Fellaini Unveiling - Old Trafford(09 of10)
Open Image Modal
New Manchester United signing Marouane Fellaini during a photocall at Old Trafford, Manchester. (credit:PA)
Soccer - Barclays Premier League - Manchester United Press Conference - Marouane Fellaini Unveiling - Old Trafford(10 of10)
Open Image Modal
New Manchester United signing Marouane Fellaini during a photocall at Old Trafford, Manchester. (credit:PA)
Fellaini worked under Moyes for five seasons at Everton but invariably played as a target man, even though his manager admitted he would thrive as a midfielder in the long-term.
A regular thorn in United's side as a blue, the 25-year-old is relieved his transfer finally went through.
"Sometimes I thought there was no chance [of the transfer happening] but in the end I was so happy to join United," Fellaini said.
Open Image Modal
Fellaini scored three goals against United for Everton
"I can play defensive or attacking - whatever helps the team. The most important thing is to win the game."
Fellaini should make his United debut in their home fixture against Crystal Palace on Saturday.
The likelihood is he will be a regular partner for Michael Carrick, United's most consistent performer the last two campaigns, due to the paucity of midfield options.
United failed with bids for Cesc Fàbregas, Ander Herrera, Daniele de Rossi and Sami Khedira during a disastrous transfer window in which both Moyes and, in particular, executive vice chairman Ed Woodward were subjected to criticism.