Widely regarded as one of baseball's top executives, Dombrowski will try to reverse the fortunes of a franchise that went 66-96 last season for an unprecedented eighth straight losing season.
The Detroit Free Press reported Monday that "all indications" point to the Tigers retaining general manager Randy Smith, who has two years left on his deal.
According to the Free Press, Dombrowski chose the Tigers over two other options -- becoming general manager of the Toronto Blue Jays or remaining president and GM of the cost-conscious Marlins, with whom he had two years and more than $2 million left on his contract.
Dombrowski became general manager of the Marlins in 1991, 18 months before the franchise played its first game, and built a team that won a World Series in 1997, a feat unmatched until the Arizona Diamondbacks won the title Sunday night in just their fourth year.
A graduate of Western Michigan, Dombrowski was able to rebuild the Marlins by acquiring quality young players in return. The Marlins finished 10 games below .500 this season.
Whether Dombrowski can lead the Tigers out of their current misery depends on whether owner Mike Ilitch will make a significant increase in the payroll, which ranked 22nd among 30 teams.
Dombrowski replaces Ilitch, who appointed himself president when John McHale left the Tigers for the Tampa Bay Devil Rays.
The 44-year-old Dombrowski also was a candidate for a similar position in Texas that went to John Hart. Dombrowski's interest in moving elsewhere come amid reports that the Marlins are among the teams being considered for contraction by Major League Baseball.
Dombrowski came to Florida from Montreal, where he was general manager of the Expos. He built a team that had the best record in baseball in 1994 when a strike aborted the season at the two-thirds mark.