Both the Rangers and Richards' agent, Pat Morris, confirmed the move.
Richards, 34, had six years remaining on his contract, paying him an average of $6.67 million per season. He signed a $60 million, nine-year deal with the Rangers in the summer of 2011.
"Tough last few days," Richards said in a statement. "I loved being a Ranger and living in New York and playing at MSG in front of great fans. ... (President and GM) Glen Sather, the management and owner, Mr. Dolan, are all class acts. I want to thank them for letting me be a part of New York life and the Rangers family."
As per the buyout rules, Richards will get two-thirds of the $19 million remaining in salary (a total of $12.6 million, paid out over the next 12 years) on his deal plus the full $8 million still owed in signing bonuses that are due over the next three summers. Once everything is paid out, Richards will have been paid about $51 million. (He made just over $2 million in salary last season during the lockout year out of his $4 million salary.)
He didn't have to clear waivers before the buyout because his contract had a no-movement clause.
Richards was a popular leader on a Rangers squad that surprised many in reaching the Stanley Cup finals this season before losing to the favored Los Angeles Kings. The Rangers also reached the Eastern Conference finals in 2012, losing to New Jersey.
But this is the last summer for NHL teams to take advantage of compliance buyouts, which don't count against the salary cap. The Rangers had to make a difficult financial decision to give them more cap/payroll flexibility moving forward, even though they valued Richards as a person and player.
Sather called the decision "extremely difficult," adding that Richards' "leadership and guidance for our young players was invaluable."
The native of Murray Harbour, Prince Edward Island, had 51 points (20 goals and 31 assists) in 82 regular-season games this season and added five goals and 12 points in 25 playoff games.
He now becomes an unrestricted free agent, able to sign with any of the other 29 NHL teams starting July 1, but is not allowed to re-sign with the Rangers.
The Associated Press contributed to this report.