Eberle has scored at least 20 goals in each of the past four seasons, and had a career-high 34 in 2011-12. But he had just two assists in 13 playoff games this spring and was panned by fans and critics for his lacklustre play.
Eberle is entering the fifth year of a six-year contract worth US$36 million and had been a frequent subject of trade rumours.
"It’s something I’ve never gone through before, it’s a different experience," Eberle said on a conference call. "But it’s something I definitely knew would eventually come. For me right now, I’m definitely excited to be a New York Islander."
The Oilers selected Eberle with the No. 22 pick in the 2008 NHL Entry Draft. He has 165 goals and 217 assists over 507 career NHL games, all with Edmonton.
"We’re excited to add a proven offensive weapon like Jordan to our lineup," Islanders president and general manager Garth Snow said in a statement. "He brings speed and a knack for scoring not only consistently, but scoring big goals, in big games.
"Jordan brings leadership and experience into our room, qualities that will continue to help us build towards our goals of being a consistent playoff contender and winning the Stanley Cup."
The move frees up cap space for the Oilers, who have some big-money signings coming up. Rising star Leon Draisaitl is due for a huge raise when his entry-level contract finishes July 1 and league MVP Connor McDavid is entering the final year of his entry-level deal.
"I think moving forward this will be a new chapter, it’ll be great with a new fresh start and a new team," Eberle said.
Strome, meanwhile, was selected fifth overall by the Islanders in 2011. He had 30 points (13-17) in 69 games last season and has 126 points (45-81) in 258 career games.