The deal carries an annual average value of $6 million, according to Arthur Staple of The Athletic.
The 27-year-old Nelson is coming off a career-high 53-point season. He played an integral top-six role for a surprise Islanders team that finished second in the Metropolitan Division and then contributed four goals - including two game-winners - in eight playoff contests.
After being selected by the Islanders with the 30th overall pick in the 2010 draft, the 6-foot-3 center has racked up 241 points in 480 career games.
Nelson was set to become an unrestricted free agent on July 1.