The deal is worth $3 million, plus playoff bonuses that could result in an additional $1 million, sources tell ESPN.
The 35-year-old center signed a one-year deal with the Chicago Blackhawks for $2 million after reaching the Stanley Cup finals with the New York Rangers in 2013-14. He had 12 goals and 25 assists in 76 games for the champion Blackhawks.
Richards played in all 23 playoff games, accruing three goals, 11 assists and a plus-4 rating.
Richards was drafted 64th overall in 1998 by the Tampa Bay Lightning, whom he led to the franchise's lone Stanley Cup title in 2003-04. Richards claimed the Conn Smythe Trophy as playoffs MVP for his contributions to Tampa's run.
Last June, Richards was bought out of a nine-year, $60 million pact he made with the Rangers in 2011, enabling him to join the Blackhawks for their title run.
ESPN.com's Pierre LeBrun and Craig Custance contributed to this report.