Following the final game of last season, themed as a French day in his honour, the midfielder admitted feeling that his footballing future lay away from Cappielow.
But Bachirou, 22, who won the Tele Top Man award for his performances over the course of the 2011/12 campaign, has performed a U-turn and agreed to return to Greenock for a third consecutive season.
The club have filed the necessary paperwork with the SFA, meaning the Frenchman could take a place in Allan Moore's matchday squad for tomorrow's visit to Hamilton Accies should the deal be processed in time.
Speaking exclusively to the Tele tonight, Moore said: "I'm delighted to confirm that we've agreed a deal with Freddy.
"He signed earlier today, and I know he's delighted to be back at Morton too.
"We've completed the paperwork and are hopeful he'll be available for the game against Hamilton tomorrow.
"If not, we might be able to list him as a trialist. But we'll get that confirmed tomorrow."
The Ton boss also revealed that he has not yet finished rebuilding his squad.
He added: "We are actively looking for another striker, and that's likely to be a loan signing.
"I have people in mind and have contacted clubs, but there is nothing to report there at this moment in time."