The Rangers confirmed in a statement the 38-year-old Swede, regarded as one of the greatest goalies in NHL history, had been paid the final year of his seven-year contract extension inked in 2013.
The buyout means Lundqvist is free to sign with any team when the free agency period gets under way on October 9.
"THANK YOU FOR EVERYTHING!," Lundqvist wrote in a social media post.
"15 years ago, I played my first game for @NYRangers I came here with high hopes and big dreams but in my wildest imagination, I could never have pictured the amazing ride that lay ahead.
"Representing this organization has been the biggest source of pride and joy in my life. 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. From the bottom of my heart, thank you!"
Lundqvist, a member of Sweden's 2006 Winter Olympics gold medal-winning team, went 459-310-96 with a 2.43 goals-against average during 887 games for New York.
He is sixth in NHL history for wins, seventh in saves and eighth in games played, which included 871 starts.
"Few players have been as important to the Rangers franchise as Henrik Lundqvist, and we are incredibly grateful for all he has done for our organization," said James Dolan, the executive chairman of MSG Sports, which owns the Rangers.
"Over his 15-year tenure, he not only established himself as one of the best goaltenders to ever play the game, he has also been one of hockey's fiercest competitors and most effective ambassadors.
"He will always be a part of the Rangers family."
Rangers president John Davidson paid tribute to Lundqvist as "one of the greatest goaltenders in hockey and one of the best players in the history of our franchise."
"We all wish Henrik and his family the best going forward," Davidson said.