The Belgium international followed Moyes from Everton to Old Trafford, securing a £27.5 million deal on deadline day after a lengthy pursuit.
And the Scot's right-hand man has no doubts over Fellaini's ability to step up and make his mark on United's squad.
"I am sure Marouane will settle in very quickly and be an integral part of United’s success in the future," Round told The Manchester Evening News.
"He is a regular scorer with really good physical presence.
"When David came here he looked at the squad and thought one of the players we needed to bring in was someone with those physical attributes in the middle of midfield who could give us strength and aggression in certain games and maybe allow one or two of the others to play.
"That, coupled with his ability to score, made him feel Marouane would be a really good acquisition for United."
Fellaini scored 11 goals in 31 Premier League appearances for Everton last season, showing another side to his game after mostly turning out as a defensive midfielder.
And Round believes his addition will provide Moyes with even more variety in midfield as he goes about replacing Alex Ferguson as the boss at Old Trafford.
"When you get to work with him every day, you get to realise that technically he is excellent. His feet and his technique work are really good. He is aggressive and tackles. He also has great fitness stats.
"He is a lot better footballer than he gets credit for and he has good passing ability.
"He doesn’t have the same range as a Michael Carrick in his long passing but his continuity and the way he keeps the ball and short passing is very good
"When you are building a squad to compete on all fronts you don’t want every single player to be the same. You want options and differences.
"It has given the manager options he didn’t have before.
"Marouane was ready for this step up. He’ll fit in well with the professionalism here and relish the challenge.
"He is a 10-15 goals a season man and that is good from midfield."
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