Postecoglou was appointed on a rolling 12-month contract last summer on the back of a trophyless campaign that saw Celtic finish 25 points adrift of Rangers in the title race having been dumped out of the cups by their Glasgow rivals and Ross County.
Few gave the Greek-born Australian a chance of turning things around so quickly but Postecoglou has confounded his critics by all but securing the title with two matches remaining after delivering the League Cup in December.
The former Australia head coach will now lead Celtic into the Champions League group stages next season and Nicholas, who admits he has been proved wrong by the manager’s performance, believes the 56-year-old must be offered a new, improved deal.
In his Daily Express column, Nicholas wrote: "Celtic's number one priority over the coming weeks should be rewarding Ange Postecoglou with a new contract.
"The Australian joined last June on a 12-month rolling deal, but the club would be absolutely crazy if talks haven't already started or been scheduled with their manager.
"Given what he has achieved in his first season in Scottish football - the league title all but sewn up to go with the Premier Sports Cup trophy bagged in December - Postecoglou merits a long-term arrangement.
"I don't think Postecoglou will be pushing for a pay rise but it would be thoroughly deserved for the remarkable job he has done so far.
"Not only will Celts make tens of millions from Champions League group stage football next season, he has also built a squad of genuine value.
"It's also worth remembering he has done it while working with the coaching team that was already in place - John Kennedy, Stephen McManus and Gavin Strachan.
"Given how dominant Rangers were last season, I doubt many Hoops supporters would have predicted their team would be on the verge of a double when Postecoglou walked in the door.
"I have to hold my hands up and admit I was unsure. I think Postecoglou was unsure as well."