Owner Bob Wetenhall announced Monday that Trestman's contract, which was to expire at the end of this season, has been extended by four years.
Should he remain until it concludes in 2016, he will have coached the Canadian Football League club for nine seasons, one more than Douglas (Peahead) Walker's team-record eight-year stint from 1952-59.
"I asked him to stay," Wetenhall said. "He's an extraordinary human being, a great friend and a great coach and I want him to stay here."
Since taking over as head coach from general manager Jim Popp in 2008, Trestman has not had a losing season. He has compiled a 50-25 regular season record, including 2-1 this season, and a 5-2 mark in the playoffs, reaching the Grey Cup game three times and winning in 2009 and 2010.
It seems every year there are rumours he will land the NFL head coaching job that has eluded him thus far, but no one connected with the Alouettes would say if his deal includes a clause that would allow him to leave.
''We've never discussed it; we're not going to,'' Trestman said.
The 56-year-old Minnesotan arrived in the CFL after a long career as a quarterbacks coach and offensive co-ordinator in the NFL and U.S. university football. He quickly learned the 12-man game and built one of the league's most powerful offences around veteran quarterback Anthony Calvillo.
The Alouettes set a team record with 15 wins in 2009, when he was named CFL coach of the year.
They dropped to 12 wins in 2010, but still won the Grey Cup, and then took a dip to 10-8 last season when injuries ravaged the defence. But they still led the CFL in scoring while Calvillo set career records in passing, completions and touchdown passes.
''I just love everything about this league,'' the 56-year-old Trestman said. ''I've enjoyed every minute.
''We've had success on the field because of Anthony. And the people I (work with) all do a great job. That allows me the low-maintenance job of being head coach.''
Trestman has a deal with Wetenhall to live in Montreal only during the season. The off-season is spent with his wife and children in Raleigh, N.C., although they fly up to visit from time to time.
His wife Cindy was at the news conference when the contract extension was signed.
''It's been a great environment for being able to do what we love to do professionally and having the off-season that Bob's provided in terms of me being at home with my family,'' Trestman said. ''My youngest will be going to college.
''It's been such an enjoyable ride, we want to stay on it for now.''
Before Trestman, the Alouettes had many winning regular seasons, but had only one Grey Cup under coach Don Matthews in 2002 since the team's rebirth in 1996.
''He put us over the hump,'' Calvillo said. ''We won two more championships under his leadership.
''To me, that's the difference. There's a lot of great players in the league. It all comes down to coaching.''
Calvillo, who will turn 40 in August, said Trestman has helped him extend his career.
''The difference is the detail in every play,'' he said. ''Each play has its own unique drop to it, it's own landmarks where each receiver has to be. And it's just drilled into us so it becomes second nature.''
Longevity at the top has been a big part of the Alouettes' success.
General manager Popp has been with the team since it moved to Montreal from Baltimore in 1996. Wetenhall took over from Jim Spiros as owner the following season. Calvillo has been with the team since 1998 and has been the starter since 2000.
Now Trestman looks to be in for a long stay, although things can change quickly in pro sports, especially when it involves coaches.