The Tykes have given Wolves the go-ahead to enter talks with the 23-year-old full-back, who has had a medical and is discussing personal terms with the west midlands club.
Wolves head coach Kenny Jackett told the club's official website: "We have agreed a fee with Barnsley and Scott's here for a medical and to sort out personal terms."
Bristol-born Golbourne, a left-sided player, progressed through Bristol City's academy before joining Reading in 2006.
He moved on to Exeter and was signed by Barnsley for an undisclosed fee in January 2012.
Golbourne missed the final two months of last season after damaging knee ligaments but returned to action in time for the start of the current campaign and has started in all six of the Tykes' matches.