Eberle, 27, has spent his entire seven-year career with Edmonton. He had 20 goals and 31 assists last season. His best season came in 2013-14, when he had 65 points.
"I'm excited. The Islanders are a tough team to play against and have a lot of potential," Eberle said, according to the Islanders. "I'm excited to be part of that."
Eberle has two years left on his contract with a cap hit of $6 million each season. The Oilers need to conserve cap space to offer big contracts to Connor McDavid and Leon Draisaitl. McDavid, the league MVP, is entering the final year of his entry-level deal.
"We're excited to add a proven offensive weapon like Jordan to our lineup," Islanders 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 Islanders are trying to build a winner for next season to convince star John Tavares to re-sign with the club. He's in the last year of a six-year contract.
Strome, 23, has one year left on his deal with a cap hit of $2.5 million. He had 13 goals and 17 assists last season. His best season was 2014-15, when he had 50 points.
He was the fifth overall pick in the 2011 draft. Edmonton know has three of the top five picks in that draft on the roster. The Oilers took Ryan Nugent-Hopkins first and acquired defenseman Adam Larsson, the fourth pick in 2011, last offseason.