"Richard is a proven offensive talent," Islanders GM Garth Snow said in a statement. "When you can add a player with his skill and competitiveness for a playoff push at a fair cost, you do it. We believe Richard will fit in well with our team."
Zednik will be an unrestricted free agent July 1 and was unable to come to terms on an extension with the Capitals.
The 31-year-old Slovak had 18 points (6-12) in 32 games with the Caps, missing half the season through injury.