The 28-year-old forward had 51 points (28 goals, 23 assists) in 82 regular-season games with the Islanders last season and four points (one goal, three assists) in eight Stanley Cup Playoff games.
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"Today's a wonderful day," Lee said. "My wife and I, we couldn't be happier. This is the place we always wanted to be and always saw ourselves. We couldn't be more thrilled than we are right now."
Lee, who was named Islanders captain Oct. 4, has led them in goals in each of the past three seasons, including an NHL career-high 40 in 2017-18. Selected by New York in the sixth round (No. 151) of the 2009 NHL Draft, Lee has 258 points (152 goals, 106 assists) in 425 regular-season games and five points (one goal, four assists) in 13 playoff games.
"It's extremely important," general manager Lou Lamoriello said. "He was our captain and still is our captain. We didn't bring him back. He never left."
Lee said, "It's a process that always seems to work itself out. I always told (agent) Neil (Sheehy) just keep working with Lou, we'll figure this out and those two would hammer it out. Obviously, it took a little bit of time, but that's just how these things work.
"There were some up and downs, but at the end of the day, I knew that we would figure this all out together."
The Islanders also agreed to terms on a one-year contract with forward Tom Kuhnhackl. Financial terms were not released.
Kuhnhackl had nine points (four goals, five assists) in 36 regular-season games and three assists in eight playoff games. Selected by the Pittsburgh Penguins in the fourth round (No. 110) of the 2010 NHL Draft, the 27-year-old has 48 points (15 goals, 33 assists) in 204 regular-season games with the Islanders and Penguins, and 10 points (three goals, seven assists) in 55 playoff games.
NHL.com deputy managing editor Brian Compton contributed to this report
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