The forward had 12 goals and 13 assists in 69 games with New Jersey last season. The Russian was especially effective in shootouts, scoring eight times in 12 chances.
"Viktor brings a lot to the table," Islanders general manager Garth Snow said. "He can be a center or wing on any of our top three lines and be solid in all zones. This is an excellent addition for our team as we head into training camp."
The deal was announced one day after the Islanders re-signed goalie Rick DiPietro to a 15-year contract worth $67.5 million, believed to be second-longest in North American sports history.
The Islanders open camp this week in Nova Scotia.
Kozlov, who also had stints with San Jose and Florida, scored 144 goals and set up 247 others in 668 NHL regular-season games. The 31-year-old center-right winger was chosen by San Jose with the sixth pick in the 1993 draft.
In nine NHL seasons with New Jersey, Nashville, the New York Rangers and Atlanta, the 34-year old Dunham has a goals-against average of 2.69. He was 8-5-0 with a 2.77 GAA.
Dunham was limited to just 17 games last season with the Thrashers because of groin problems and went 8-5-0 with a 2.77 GAA and .893 save percentage.
The Islanders are searching for a veteran backup to DiPietro.
Park, a native of South Korea, had eight goals and 10 assists in 60 games for Vancouver last season. He spent the previous three campaigns with the Minnesota Wild and recorded 37 goals and 37 assists in 217 games.
Information from The Associated Press and SportsTicker was used in this report.