Scotland international McGregor joined the Tigers from Turkish side Besiktas for £1.5million in the summer.
The former Rangers No.1 has conceded seven goals in his first seven Premier League matches - including three clean sheets.
Rosenior said: "He's a fantastic goalkeeper. You can see why he's played for his country.
"It was a great bit of business from the gaffer to sign him.
"I can't think of many goalkeepers I would take over him.
"He exudes confidence and spreads that to the back four.
"A lot of our good performances have started from him and I'm enjoying playing in front of him."
Steve Bruce's side have made a good start to life back in the top flight and currently sit in eighth position with 11 points from seven matches.
Rosenior believes the Tigers are capable of maintaining their good run of form after the international break.
"I'm not surprised with where we are because I know the quality we have at the club," he said.
"We need to keep our underdog mentality going and I think we're underrated because every team we've played this season has known they've been in a game."
McGregor, 31, made more than 200 appearances for Rangers before moving to Turkey in July 2012.