Naslund, who left the Vancouver Canucks last summer as a free agent, signed a two-year deal worth $8 million with the Rangers but decided to skip the final season when he will be 36.
The five-time All-Star spent parts of 12 seasons with the Canucks and was brought to New York by general manager Glen Sather after the Rangers failed to re-sign captain Jaromir Jagr.
Naslund played all 82 games this season, recording 24 goals and 46 points, but he had only one goal and two assists in the Rangers' seven-game loss to Washington in the first round of the playoffs.
"I would like to sincerely thank Glen Sather and the New York Rangers for giving me the opportunity this past season in New York," Naslund said. "I would also like to thank the Vancouver Canucks and all of their fans for their support over the 11-plus seasons I was a part of their organization, as well as to the Pittsburgh Penguins where I began my NHL career."
Naslund scored a career-high 104 points -- including 48 goals -- during the 2002-03 campaign when he won the Lester B. Pearson Award as the NHL's most outstanding player as chosen by his peers, but his numbers went down each of the next five seasons.
Naslund, who served as captain of the Canucks for eight seasons, was chosen with the No. 16 overall pick in the 1991 draft by Pittsburgh and spent three seasons with the Penguins before being traded to Vancouver in 1996.
The announcement by the Swedish left winger will help the salary-cap challenged Rangers, who will now have more flexibility to add to an anemic offense that scored only 11 goals in the postseason loss to the Capitals.
In 1,117 regular-season NHL games, Naslund had 395 goals and 869 points. He reached the 40-goal mark three times and scored at least 30 in six seasons.
Naslund played in 52 postseason games, recording 14 goals and 36 points.