Dons legend and Director of Football Willie Miller announced that Clark had rejected the offer of a new contract at the club at a press conference on Traitors' Tuesday, adding that a bid of £100,000 from Paul Sturrock's club had been rejected.
But an increased bid of around £200,000 has now been accepted by Aberdeen and Clark is now likely to join fellow contract rebel Michael Hart at Home Park.
Right-back Hart, like fellow 27-year-old Clark, is out of contract in the summer and also has been given the green light to leave the Dons.
Aberdeen are believed to have accepted a £175,000 offer from the Pilgrims for vice-captain Hart, who is stalling over terms with the club until he has spoken to other Championship clubs.