Financial terms were not disclosed, but Newsday reported de Haan's contract is worth $5.9 million and Cizikas' is worth $2 million.
The Islanders selected de Haan with the 12th pick at the 2009 NHL Draft. He played in 51 games for New York last season and had three goals and 13 assists. The 23-year-old started the season with the Bridgeport Sound Tigers in the American Hockey League and had one goal and two assists in 17 games.
Cizikas, 23, had six goals and 10 assists in 80 games for the Islanders last season, and has 12 goals and 23 assists in 140 NHL games. He was New York's fourth-round pick (No. 92) in 2009.