Smith left Old Trafford in 2004 to join Newcastle United, where he worked with Round during Sam Allardyce's tenure at St James' Park.
"I've worked with Steve Round at Newcastle and he's a great coach," Smith told ManUtd.com. "I know a lot of the lads respect him as a coach and I spent a good bit of time at Newcastle with him and he's very thorough in what he does. I think he will prove to be an asset to Manchester United.
"Sir Alex Ferguson will have done his homework on who to appoint and who to bring in to take over the mantle. My experience of Steve Round is he's a great coach, who is enthusiastic as well and I think, over the years to come, he's sure to develop into a great asset to the club."