The team announced that Lamoriello will have "full authority over all hockey matters."
In three seasons as GM, Lamoriello led Toronto to a pair of playoff appearances; however, it was unable to advance past the opening round.
Prior to his stint with the Maple Leafs, Lamoriello spent 28 years in the New Jersey Devils' front office as team president and general manager.
During his time with the Devils, Lamoriello reached the Stanley Cup Final five times, won the Stanley Cup on three occasions (1995, 2000, 2003) and was inducted into the Hockey Hall of Fame as a builder in 2009.
Upon hiring Lamoriello, Islanders co-owner Scott Malkin said, "We are committed to giving Lou every resource and the full support of the entire organization as we pursue our program to compete at the highest level."
The 75-year-old Lamoriello is joining an Isles organization that has missed the playoffs in each of the past two seasons after making it in 2014-15 and 2015-16.
His main priority to start will likely be to retain forward John Tavares in free agency.
Tavares, 27, is an All-Star player in his prime who is coming off one of his best seasons, as he registered 37 goals and 47 assists for 84 points in 2017-18.
New York also has two first-round and two second-round picks in June's draft.
Provided Lamoriello can prevent Tavares from going elsewhere on the open market, he will take over a talented roster with a legitimate shot at returning to the playoffs next season.