The stopper recently joined Kenny Jackett's side from Championship rivals Fulham.
The former Leeds stopper has signed a two-year contract with Wolves after they agreed an undisclosed fee with Fulham, the Express and Star claims.
And while Ikeme's form has left his new rival for the number one spot hugely impressed, the 32-year-old claimed that he does not plan to settle for being the Nigeria international's understudy.
"In my opinion Carl is comfortably one of the top three keepers in the league," he told the Express and Star. "It is up to me to put pressure on him. Obviously I want to play - everyone wants to play - and everywhere I have been it has been a challenge.
"You just have to be patient if you are waiting for your chance and take it when it comes along."
With Emiliano Martinez's loan coming to an end, the side were looking extremely thin in the goalkeeping department, and having two stoppers with bags of experience in the second tier should greatly benefit the club's hopes of putting themselves in the promotion picture next season.
And after a season where injuries played a key role in the side being unable to mount any kind of play-off charge, Wolves supporters will be hoping that Lonergan is the first of many signings that see the squad go into the next campaign with the kind of depth that would allow them to cope even if they once again lose several players to injury.