The former Southampton man had attracted interest from West Brom and Fulham, but Wolves have stolen a march on their rivals by jumping to the head of the queue for van Damme's signature.
Van Damme was believed to be in attendance for Wolves' final home game of the season against Sunderland last weekend and he is expected to tie up his move to Molineux in the near future.
The 26-year-old revealed Mick McCarthy's desire to sign him played a big part in his decision to make the move to Wolves.
"I have been in contact with them for a long time and Mick McCarthy was very insistent," van Damme was quoting as saying in The People.
"That gave me a good feeling."