Schneider, a 34-year-old goalie, was an unrestricted free agent and joins an Islanders roster that includes goalies Semyon Varlamov and rookie Ilya Sorokin. Thomas Greiss, who shared time with Varlamov last season, agreed to a two-year contract with the Detroit Red Wings on Oct. 10.
The New Jersey Devils bought out the remaining two seasons of a seven-year contract Schneider signed July 9, 2014. He was 3-6-2 with a 3.53 goals-against average and an .887 save percentage in 13 games (11 starts) last season and played 14 games for Binghamton of the American Hockey League.
Schneider was traded to the Devils by the Vancouver Canucks on June 30, 2013 for a first-round pick in the 2013 NHL Draft, which Vancouver used to select center Bo Horvat. Lamoriello was Devils GM at that time.
In seven seasons with New Jersey, Schneider's 115 wins are third in its history, behind Martin Brodeur (688) and Chris Terreri (118), and his 17 shutouts and 311 games as a goalie are second to Brodeur (124 shutouts, 1,259 games).
Schneider had surgery to repair a core muscle injury in May 2016, and surgery to repair torn cartilage in his left hip two years later. He's 9-19-6 with a 3.22 GAA and .897 save percentage in 39 games the past two seasons.
Selected by the Canucks with the No. 26 pick in the 2004 NHL Draft, Schneider is 170-159-58 with a 2.43 GAA, .918 save percentage and 26 shutouts in 409 games (388 starts) for the Canucks and Devils.
Greene, a 38-year-old defenseman, scored 14 points (two goals, 12 assists) in 63 games with the Devils and Islanders last season, including three assists in 10 games after he was traded to New York on Feb. 16. Greene scored four points (two goals, two assists) in 21 Stanley Cup Playoff games.
Signed by New Jersey as an undrafted free agent on April 4, 2006, Greene has scored 249 points (49 goals, 200 assists) in 933 games with the Devils and Islanders and 13 points (five goals, eight assists) in 71 playoff games.
Greene, who ranks sixth all-time on the Devils in games played (923), was captain for five seasons from 2015-20.
Martin, a 31-year-old forward, scored eight points (five goals, three assists) in 55 games with the Islanders last season and six points (five goals, one assist) in 22 playoff games.
Selected by New York in the fifth round (No. 148) of the 2008 NHL Draft, Martin has scored 131 points (61 goals, 70 assists) in 692 games with the Islanders and Toronto Maple Leafs and 10 points (six goals, four assists) in 60 playoff games.