Morrison and Ottawa's Ivanie Blondin were also crowned season champions in their respective World Cup disciplines, the men's 1500 and the women's mass start, while Dubreuil finished second in the 500 standings for the season.
Morrison, from Fort St. John, B.C., won gold in the men's 1,000 on Saturday and captured Sunday's race in one minute 46.15 seconds, in what was the last meet of the season.
"All I did was to skate a solid race, without trying to do anything special. I didn't go too easy, or try too hard. I was in a good pairing and did some fast laps the entire way through, and I had a good finish," Morrison said, who won bronze in the 1,500 race at the Sochi Olympics.
"It was such a surprise to win the season title," added Morrison. "It was a goal of mine in 2007 and 2013, but being injured in 2013 put an end to any chance of that happening. Racing to a win at a clutch moment paid off big time and I couldn't be happier to have achieved one of my career goals today, one that I thought might never happen."
Heather Richardson clinched the women's overall speedskating World Cup title with a fourth-place finish in the mass start. The American finished with 1,195 points in the overall standings, 99 more than Martina Sablikova of the Czech Republic, who won the race in 9:1.76.
Blondin placed eighth and finished with 466 points, ahead of Dutch skater Irene Schouten on 432 after finishing 16th.
"I was going for the season title and I did it - I even was part of the last sprint at the end. I'm quite happy about the result," Blondin said. "This title is a big deal for me. I would have liked to have won the world title at the World Single Distance Championships, but I finished second. Today is like a consolation prize."
Ruslan Murashov of Russia won the second men's 500 of the weekend, clocking 34.97 to edge both Dubreuil of Levis, Que., and Michel Mulder of the Netherlands by 0.13.
With files from the Associated Press