Richards indicated on his Twitter account he has inked a deal with the Rangers, writing, "Very happy to become a New York Ranger today!!! Playing at MSG will be amazing and looking forward to working with a great young team."
The New York Daily News reported Richards' deal was for $58 million over nine years.
The team had not released an official statement Saturday.
Richards, 31, considered the top free agent on the NHL market this year, has played for the Dallas Stars during the past three seasons after being traded there from Tampa Bay in February 2008.
The Prince Edward Island native won a Stanley Cup title with the Lightning, during which he earned the Conn Smythe honors as playoff MVP. He has racked up 220 career goals and 496 assists for 716 points in 772 regular-season games.
Last season with the Stars he compiled 28 goals and 49 assists for 77 points in 72 games.