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Having already won the Austrian Cup, Salzburg took an unassailable 11-point lead over LASK Linz to complete the double.
Marsch is the former coach of MLS side New York Red Bulls but departed in 2018 to become an assistant at German club RB Leipzig. He then was named manager at Salzburg at the beginning of this season.
Linz slumped to a 1-0 defeat at Wolfsberger with two games to spare, allowing Salzburg to continue their dominance over the Austrian Bundesliga. They also took their league tally to 102 goals in 30 games.
Linz led at the end of the regular season -- when the 12 teams meet twice -- but then had six points deducted, later reduced to four on appeal, for breaking coronavirus regulations.
The squad was filmed staging full training sessions during a period when the coronavirus rules restricted them to training in small groups.
Linz won only three out of eight games in the final stage, which features the top six teams.
Andre Ramalho headed Salzburg ahead at the end of the first half from a corner, Hwang Hee-chan added the second in the 53rd minute and then set up the third for Patson Daka to volley home six minutes later.
An 89th minute penalty converted by Shon Weissman gave Wolfsberger three points in Linz.
Why managing Dortmund could be too big a jump for Marsch
Ale Moreno questions if Jesse Marsch is ready to leave RB Salzburg to take on a job like Borussia Dortmund.