The Islanders will leave their traditional home base at Nassau County on Long Island when their current lease expires after the 2014-15 season.
They will relocate to Brooklyn and share the Barclays Center, a brand new multi-purpose indoor arena, with the National Basketball Association's Brooklyn Nets.
"Today we are announcing that the New York Islanders will remain in a local marketplace as we have entered into 25-year agreement beginning with the 2015-16 season to play in this state of the art building called Barclays Center," team owner Charles Wang said.
The announcement follows years of debate over the long-term future of the Islanders at the Nassau Veterans Memorial Coliseum, which was opened in 1972 when they were admitted to the NHL.
Plans to renovate the stadium or build a new one were considered then rejected, prompting speculation they could shift to Brooklyn along with the Nets, who were previously based in New Jersey.
"I am excited about today's announcement and look forward to a long successful future in Brooklyn," said Wang.
"It was our goal from day one to keep the Islanders in the local New York area."
Founded in 1972 as part of a strategy to stop the rebel World Hockey Association getting a foothold in New York, the Islanders have been based at Nassau since their admission.
They are one of three NHL teams in the New York area, along with the New York Rangers and New Jersey Devils.
Led by Hall of Famers including Denis Potvin and Mike Bossy, the Islanders were an overnight success, making the playoffs in 14 consecutive seasons between 1974 and 1988, and winning the Stanley Cup four times in a row from 1980 to 1983, earning official recognition as an NHL dynasty.
In recent times, the team has fallen on hard times, finishing last in the Atlantic Division in each of the past five seasons and failing to make the playoffs, triggering dwindling attendances.
The 2012-13 NHL season was due to start earlier this month but remains on hold because of a labor dispute between the league and players.
The 675,000-square-foot, 18,000-seat Barclays Center was officially opened on September 28 with a concert by rapper Jay-Z.
Built on the site of a gritty former rail yard, the arena sits in the middle of a busy shopping area.
The Nets will play their first regular-season game at the arena, against the New York Knicks, on November 1.