The one-year deal is worth $2 million, a source confirmed to ESPN.com.
"It's a big moment for us to be able to add someone of his caliber as a hockey player and as an individual," Blackhawks general manager Stan Bowman said on a conference call. "He brings so many things to the table for us. He's certainly got the experience and leadership. I think his character off the ice is something (that) sometimes gets overlooked and is important to us. He's got sort of the whole package we're excited about."
The 34-year-old center was a key part of the Rangers' surprising run to the Stanley Cup finals this spring, acting as the de facto captain for the Blueshirts despite the uncertainty of his future in New York.
Richards, who had the remaining six years of a nine-year, $60 million contract with New York bought out to free up needed cap space, now joins a strong Blackhawks team that has been looking for help down the middle.
"If I was going to go to Chicago, it was going to be this way," Richards said on a conference call. "I didn't go into free agency thinking anything. I was very flexible coming in because I'm pretty confident I can still play a lot of hockey in this league. I just went to the Stanley Cup final. You get the itch when you get that far. You want to win.
"I saw an opportunity to play on a great team and fill a role, but also these guys are relevant every year. I just thought this was a great fit. It wasn't trying to be here long term. If it's one year, that's fine. Hopefully we can make it work. Who knows what can happen down the road. I can't predict that. I'm not really worried about it. I want to get there and enjoy this opportunity."
The Blackhawks, who were just one goal shy of making it to the Stanley Cup finals themselves after losing in overtime of Game 7 of the Western Conference finals to the eventual champion Los Angeles Kings, have been searching for a center to add via trade or free agency.
With Ryan Kesler traded to Anaheim last week, Jason Spezza acquired by the Dallas Stars Tuesday morning, and top free-agent center Paul Statsny signing with the St. Louis Blues Tuesday afternoon, Richards remained as a cost effective candidate to fill their needs.
Richards is expected to fill the Blackhawks' need for a second-line center and play alongside wings Brandon Saad and Patrick Kane. The Blackhawks have rotated second-line centers in the past few seasons.
Richards finished with 20 goals and 51 points for the Rangers this season, his 10th NHL season in which he has posted 20 goals or more.
Though the former Conn Smythe Trophy winner had a strong start to the spring, he experienced declining production and a diminished role in the team's series against the Kings, during which he was relegated to the fourth line.
Richards still has creative playmaking ability, however, and can add veteran experience on Chicago's power play as well as inside the locker room.
Information from ESPNChicago.com's Scott Powers was used in this report.