Financial terms were not disclosed.
"Jacques, Mike and Mario have done an outstanding job of coaching our team and continue to prove they are among the best teachers in the game," said Wild General Manager Doug Risebrough.
Lemaire, named the franchise's first coach in June 2000, instilled the neutral zone trap and defensive discipline. After finishing 25-38-13-5 for 68 points in its inaugural season, Minnesota went 26-35-12-9 last season for 73 points.
This season, the Wild sit currently in the sixth playoff spot in the Western Conference with a 26-18-8-1 record for 61 points, 13 ahead of their pace from last year.
Lemaire's defensive system taking hold is the primary reason for the improvement. The Wild rank fourth in the league in fewest goals allowed with 117.
Lemaire, 57, won eight Stanley Cups as a player with the Montreal Canadiens, including four straight from 1975-76 to 1978-79, when he was a teammate of Risebrough and Tremblay.
He coached the New Jersey Devils to their first Stanley Cup title in 1994-95, espousing the neutral zone trap. He compiled a 199-122-57 record in five years as Devils coach. Lemaire began his coaching career in 1983-84 with the Canadiens, and was 48-37-12 in parts of two seasons.
Lemaire, elected to the Hockey Hall of Fame in 1984, has a career coaching record of 323-266-102.
Ramsey, 42, spent three years as an assistant with the Buffalo Sabres before joining the Wild in July 2000.
Tremblay, 46, spent three years as a scout with the Canadiens before joining Lemaire in Minnesota in July 2000.