The 29-year-old joined Ton in January 2008 but has moved to end uncertainty over his future by switching to his home-town club.
Ton have also started issuing letters to out-of-contract players clarifying the club's future plans.
Stevie Masterton and Kevin Finlayson have both been informed their contracts will not be renewed, though the new manager will be offered the chance to re-sign them.
In McGuffie's case, his contract expires today and he confirmed talks are at an advanced stage with the Dumfries side.
He said: "I've not signed yet as my contract with Morton doesn't expire until today.
"But I've been speaking to them and it looks like I will probably be playing my football there next year.
"The likelihood is that I will sign with them from 16 May. It's all looking positive."
James Grady and Allan McManus had been keen to keep McGuffie at the club but their departure made the former Gretna player's decision easier.
He said: "James and Allan were looking to keep me on but they have moved on.
"I had a couple of options down south that would have meant going on trial.
"I loved every minute of my time at Morton. I just wish we had been challenging at the right end of the table.
"That is something the fans deserve. But it is a club with a lot of potential and I'm sure it will move forward from here."
Finlayson confirmed that he received a letter from the club this week.
He said: "They said the club are not in a position to offer new contracts but that when the new manager comes in he will be given the names of the players who are out of contract and if wants to keep them he will be in touch.
"For me right now, it's a case of trying to find a new club."
Masterton is also looking to a future away from Greenock. He said: "I am actively looking to get something else now.
"I think that is me finished at Morton unless the new manager comes in and is a big fan. I'm not completely closing the door on Morton but it's in my head now that it's time to move on."
The futures of the club's other out-of-contract players will be clarified soon, though Erik Paartalu has returned to Brisbane Roar in Australia and Jim McAlister is likely to move to a Premier League side.