The former Manchester United star performed miracles in guiding Sunderland - the club Albion host on Saturday - to the Coca-Cola Championship title in his first season.
Mowbray said: "It is good for the game that Roy Keane is back in management. He showed he could do the job of getting a team out of the Championship at Sunderland.
"He did an amazing job at Sunderland. When he went in, they weren't winning many games and they went like a train through the league and ended up winning it.
"Ipswich will be hoping for a similar ride. They are a club more than geared up for the Premier League.
"They had a very successful first season a few years ago in the Premier League and finished fifth. If someone did that now, it would be some story.
"When they did it, it was before the hype that is around now.
"Everyone knows the aftermath of that - relegation, administration - but the infratructure is there and the stadium is of Premier League quality."
Mowbray added: "Ultimately you've got to earn the right to play in the Premier Leage and Roy will have 46 games to get them there next season.
"He has been there, he knows the league. It appears to me Ipswich have got an ambitious owner. Any owner who employs someone of the drive and ambition of Roy Keane is going to have to try and match it. Let's wait and see."