"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; 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."
Mulgrew joined Wolves in August 2006 as part of the deal which saw Lee Naylor move to Celtic Park.
However, Mulgrew managed just nine appearances for Wolves and spent a spell on loan at Southend.
He returned to Scotland in 2008 to sign for Aberdeen and impressed for the Dons before leaving Pittodrie when his contract expired in the summer.
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