The Celtic defender came through the youth ranks at Parkhead but failed to break in to the first team before joining Wolves in 2006 in a deal involving Lee Naylor going the opposite way.
Mulgrew struggled throughout his time in the Black Country and returned north of the border in 2008 to join Aberdeen before pitching up at Parkhead for a second time last summer.
Following last night's 2-0 friendly defeat by the midlands club at Parkhead, Wolves boss Mick McCarthy claimed the 25-year-old had looked twice the player he did at Molineux.
Mulgrew agreed with the former Celtic defender's assessment and put his progress down to his spell in England.
"I'd definitely agree with that," he said. "I've grown up a lot as a person on and off the pitch.
"I've played a lot more games now and have experience behind me which has made me a better player.
"I was a bit naive when I was at Celtic before and maybe took it for granted a wee bit.
"When you come through at a club like Celtic you're spoon-fed a wee bit and things come a bit easy.
"So I think I've grown up from going down to Wolves and I have learned a lot.
"I'm definitely a better person and a better player now."
Mulgrew added: "If I could go back I definitely wouldn't change it.
"I had a couple of bad injuries and had a wee bit of homesickness but I wouldn't change it because it definitely made me better on and off the pitch.
"I wouldn't change in anything in my career."
Improved player or not, Mulgrew will do well to pin down a place in Neil Lennon's side this season.
He shifted from left-back to centre-back in January due to an injury crisis but knows that competition in defence has been increased with the addition of Kelvin Wilson and Adam Matthews.
"There's competition all over the park but especially at centre-back but that's what you expect at a club like Celtic," said Mulgrew.
"Whoever comes here has got to expect to be up against it with the players we have already got and the players we are going to attract to a club of this size.
"It only makes the team better and we've got to be up for the challenge.
"It's a long season. There's a lot of competitions and a lot of games and you've just got to be ready when called upon.
"It could come at any point and you've got to make sure you are on your toes and be ready to take your chance when you get it."