Noel was let go after the Jets fell to 19-23-5 on the season with Saturday's 6-3 home loss to Columbus. They occupy last place in the NHL's Central Division.
He finished with an 80-79-18 record in two-plus seasons guiding the Jets since the team relocated from Atlanta to Winnipeg, missing the playoffs both seasons.
They went 37-35-10 in Noel's first season, following with a 24-21-3 mark in the lockout-shortened 2012-13 season.
Maurice, 46, takes over in Winnipeg more than two years after being fired as Carolina's head coach. Last season he coached in Russia's Kontinental Hockey League.
He sports a career NHL coaching mark of 460-457-167 with Hartford/Carolina (1995-04, 2008-11) and Toronto (2006-08). Maurice is best known for taking the Hurricanes to a 2002 Eastern Conference championship.