Mulgrew will join Celtic on a free transfer as his contract at Aberdeen had expired.
Mulgrew has signed a three-year contract with the Scottish giants.
Lennon said: “Charlie has signed and I am pretty pleased about that.”
Lennon added: “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. He’s had a couple of good seasons at Aberdeen and I’m pleased we’ve got him on board.”