Weight, 43, previously served as a special advisor to general manager Garth Snow.
He also will remain an assistant coach on the staff of coach Jack Capuano, a role he's held since retiring as a player after the 2010-11 season.
Weight played the final three of his 19 NHL seasons with the Islanders, serving as captain for the final two. A second-round pick (No. 34) of the New York Rangers in the 1990 NHL Draft, he had 278 goals and 1,033 points in 1,238 games for the Rangers, Edmonton Oilers, St. Louis Blues, Carolina Hurricanes, Anaheim Ducks and Islanders.
Weight won the Stanley Cup with the Hurricanes in 2006 and had 23 goals and 72 points in 97 Stanley Cup Playoff games.
In addition, Greg Cronin, Bob Corkum and Matt Bertani have been named as assistant coaches.
Cronin, 51, spent the past three seasons on Randy Carlyle's staff with the Toronto Maple Leafs. This will be Cronin's second stint as an Islanders assistant. He also has served as coach of the Islanders' American Hockey League affiliate, the Bridgeport Sound Tigers.
Corkum, 46, was an assistant coach at the University of Maine from 2008 to 2013. Bertani, 38, was an assistant coach this season after being the team's video coach in 2012-13.