Celtic have completed the £600,000 signing of Lee Naylor from Wolves, with Charlie Mulgrew moving in the opposite direction.
Defender Mulgrew, 20, agreed a three-year deal after passing a medical on Wednesday night.
He arrived at Molineux as a makeweight in the transfer.
Left-back Naylor, 27, has joined Celtic until the summer of 2009, with the club having the option of a further year.
It is the second time Hoops boss Gordon Strachan has plundered the Coca-Cola Championship outfit, after signing striker Kenny Miller in the summer.
Wolves manager Mick McCarthy was happy with his end of the deal following the arrival of Mulgrew.
'Charlie is a good footballer,' he said.
'He's over 6ft and is a left-sided player at either full-back or centre-back and as we've now lost Lee Naylor, he'll help cover that area.
'I'm looking forward to getting him into training and seeing what he can do.'
Celtic are also hoping to sign Dutch striker Jan Vennegoor of Hesselink.