The deal is worth $7.5 million, reports Arthur Staple of Newsday.
Nelson rejected the one-year qualifying offer New York extended to him in July, as well as the two-year deal worth under $3 million the team offered him several weeks ago.
If Nelson had not signed by 7 a.m. on Thursday, he would not have been allowed to play for the Islanders in the coming season, according to a team rule instated by owner Charles Wang. Players reported for physicals Thursday morning and will have their first training camp session on Friday.
The Islanders selected Nelson, 23, in the first round of the 2010 NHL draft, and he has since played 154 games for New York, scoring 34 goals over two seasons. Last season he scored 20 goals with 22 assists.
New York opens its season on Oct. 9 against the Blackhawks.
- Erin Flynn