The 24-year-old is Neil Lennon's first signing and ironically has been brought in to replace the departed Lee Naylor.
Former Celtic youth player Mulgrew failed to make the grade in his first spell at the club and joined Wolves in part exchange for Naylor in 2006.
Mulgrew managed just nine appearances for the Midlands club and had a spell on loan at Southend before returning to Scotland in 2008 to sign for Aberdeen where his contract expired at the end of the season.
The former Scotland Under-21 player has signed a three-year deal at Celtic where he is set to be joined by South Korea international Cha Du-ri.
"Charlie has signed and I am pretty pleased about that," said Lennon. "He was a kid who was here and went away.
"He went to play in England and had a great spell at Aberdeen and outside the Old Firm we felt he was one of the best players in the SPL.
"He gives us a bit of balance because we lack left-sided players and he has a cultured left foot."
"I am hoping that Cha Du-ri gets completed over the next couple of days" Lennon added.
"He's played in Germany for the majority of his career and we have had an eye on him for a while.
"He has 50 caps and has good experience."
The Irishman, who revealed that Koki Mizuno and Zheng Zhi have left the club, is still hoping to persuade Sol Campbell and Jimmy Bullard to come to Glasgow.
Lennon said: "It is early days (with Sol), we have had contact over the summer.
"We were delighted to get him up and talks are ongoing at the minute.
"It is not just his experience but his quality and calibre of player and personality.
"He's had to put up with a lot of troubles in his career, he has dealt with them brilliantly.
"I think he is a very proud man and those are the qualities I would like to bring to the club.
"He's had a great career but I think he still has a lot to offer.
"He's gone away to think about things and will be in touch over the next week or so.
"I've also been speaking with Jimmy," Lennon continued.
"I've had dialogue with Hull and Jimmy on a personal level and again it is still in its initial phase.
"He hasn't said yes and he hasn't said no.
"We are hoping to speak to him again over the next few days and try to get something concluded."