The Dons thought they had got his man last week only for the deal to stall with, Jimmy Calderwood claiming the Quakers had changed their demands.
However, a fee has been agreed between the two clubs and Wright, who top scored for Darlo last season, has agreed personal terms.
The Dons must wait to conclude the deal, though, as Wright is struggling with a slight knee injury and as such can't take his medical.
Calderwood told the club's official site: "(Tommy) had a small injury towards the end of last season in his knee and the doctor has taken a look at him and we are going to get him back in a couple of weeks to look at him again.
"He is in the middle of his rehab at the moment so it is difficult for the medical staff to fully access him.
"Like (recent signing) Charlie Mulgrew I have been trying for a long time to sign the player so I don't mind waiting another couple of weeks."
"In these kind of situations you can never risk even the smallest of niggles and that is why the deal is not signed and sealed."