Ilya Sorokin and three other players signed multiyear contracts with the New York Islanders on Saturday.

The contract for Sorokin is an eight-year deal, which will start after this season. He could have become a restricted free agent next July.

Sorokin was 31-22-7 with a 2.34 goals-against average, .924 save percentage and an NHL-best six shutouts in 62 games (60 starts) last season. He was third in save percentage and sixth in GAA among goalies to play at least 20 games and tied for third in games played.

"It's obvious that you don't want a player of his stature to go into the last year of his contract," Islanders general manager Lou Lamoriello said of Sorokin. "I think it's a lot of pressure on the player ... Ilya wanted to be here. We wanted Ilya to be here. There's no better time to do it."

Also signing Saturday were forward Pierre Engvall (seven years), defenseman Scott Mayfield (seven years) and goalie Semyon Varlamov (four years). Each were unrestricted free agents.

The 27-year-old made at least 30 saves in 25 games and was 5-0-2 when making at least 40 saves in a game this season. He was a finalist for the Vezina Trophy, which is awarded to the best goalie in the NHL. Linus Ullmark of the Boston Bruins won the award.

Varalmov was 11-9-2 with a 2.70 GAA, .913 save percentage and two shutouts in 23 regular-season games (22 starts) for the Islanders last season.

Selected by the Washington Capitals with the No. 23 pick in the 2006 NHL Draft, the 35-year-old Varlamov is 272-220-64 with a 2.65 GAA, .916 save percentage and 38 shutouts in 583 regular-season games (556 starts) for the Capitals, Colorado Avalanche and Islanders, and 31-27 with a 2.42 GAA, .919 save percentage and four shutouts in 60 Stanley Cup Playoff games (58 starts).

"I don't think I've seen anyone [in] any better [shape] than 'Varly,' as far as how he takes care of his body, how he prepares for each day of practice, how he post-practices and post-game takes care of his body," Lamoriello said. "He is a consummate pro, both on and off the ice. … So, he might be a 35-year-old, but I will tell you this: I've seen a lot of 26-, 27-year-olds I wish were in the shape that he is, and as far as that goes, that's the difference."

Engvall had 30 points (17 goals, 13 assists) in 76 regular-season games for the Toronto Maple Leafs and Islanders last season, including nine points (five goals, four assists) in 18 games after he was acquired in a trade Feb. 28.

The 27-year-old had two points (one goal, one assist) in six Stanley Cup Playoff games last season.

Selected by Toronto in the seventh round (No. 188) of the 2014 NHL Draft, Engvall has 92 points (47 goals, 45 assists) in 244 regular-season games for the Maple Leafs and Islanders and six points (one goal, five assists) in 23 playoff games.

"He brings speed to the game, and he's got outstanding range," Lamoriello said. "He has hockey sense, and I think he's only going to get better and better. I watched him when he first came over when I had him in Toronto, and his game has increased as far as the dimension that he has. And I think he has tremendous growth. And although it might look a little long, because of what his past situation is, I think that you're going to find dividends in this young man."

Mayfield had 24 points (six goals, 18 assists) in 82 regular-season games for the Islanders last season and three points (one goal, two assists) in six playoff games.

Selected by New York in the second round (No. 34) of the 2011 NHL Draft, the 30-year-old has 111 points (25 goals, 86 assists) in 428 regular-season games and 16 points (four goals, 12 assists) in 57 playoff games.

"I think that he's an unheralded sort of player in what he does and what he brings, the minutes that he takes, also the physicality he brings to the game," Lamoriello said. "And I think he adds that to the defense that we have. He plays in every defensive situation and also is a top penalty-killer. So, he was an important person. He doesn't do it with glamour. He just does it in an efficient way."

NHL.com independent correspondent Stefen Rosner contributed to this report