Moyes has endured a difficult start in the Old Trafford hotseat after taking over from Sir Alex Ferguson this summer.
The Scot has collected just four points from his opening three Barclays Premier League games, losing for the first time at Liverpool on Sunday, and Marouane Fellaini was his only major signing during a shambolic transfer window that ended with a failure to rush through a loan deal for Real Madrid full-back Fabio Coentrao.
Yet Round, who followed Moyes to United from Everton, extending a partnership that first began in 2008, insists these are merely teething troubles.
And he has no doubt United have chosen the right man to succeed Ferguson.
"Without a doubt, David was ready for this job," Round told the Manchester Evening News.
"He has an incredible desire to succeed. He now has the stature and presence to move to a club like this. I really do believe he will be a big success.
"Now I have been in this club and environment I can understand why Sir Alex and the board appointed him - to keep that continuity, work ethic, drive and feeling about the club going.
"It was very important to them and I can understand now that I have been here and lived it. They were made for each other."
Although Fellaini has become the fourth most expensive player in United history, there are some who worry the Belgian may not be the forceful midfield presence they believe United need.
- Sports & Recreation
- Marouane Fellaini
- Sir Alex Ferguson
- Barclays Premier League