Lundqvist spent his entire NHL career with the Rangers and holds over 50 franchise records, including the all-time mark for wins, appearances by a goaltender, shutouts, playoff appearances and playoff wins.
The 38-year-old known as "The King" also won the Vezina Trophy as the NHL's best goaltender for the 2011-12 season and was a finalist for the award in four other years.
"Representing this organization has been the biggest source of pride and joy in my life," Lundqvist, who can sign with any team when the free agent period begins on Oct. 9, wrote on Twitter.
"I'm so grateful for the opportunity, for the friendships and for all the great memories created wearing the red, white and blue. I will always cherish my time as a Ranger."
Lundqvist's playing time decreased in the recently-concluded NHL season with the emergence of rookie Igor Shesterkin.
During Lundqvist's time with the Rangers, the team advanced to the Stanley Cup Final in the 2013-14 season and reached the Eastern Conference Final three times in a four-year span.
Lundqvist, who helped lead Sweden to an Olympic gold medal in 2006, has earned more career NHL wins (459) than any other non-North American born goaltender and also reached the 400-win mark faster than any other goaltender in league history.
"From the time I met Henrik when he first came to New York in 2005, he has been the consummate professional," said Rangers President John Davidson.
"His tireless work ethic, passion for the game, and love of the Rangers and New York City enabled him to become one of the greatest goaltenders in hockey and one of the best players in the history of our franchise." (Reporting by Frank Pingue in Toronto Editing by Toby Davis)