The deal marks a return to the NHL for Richards, who had his contract with the Los Angeles Kings terminated in June. The Kings cited a breach of contract after Richards was arrested June 17 at the Canadian border. Richards was later charged with possession of a controlled substance. Richards' court date in Manitoba for that charge was moved to January. The Capitals secured a work visa for Richards to work in the United States.
Richards met with the NHL on Tuesday afternoon, a source told ESPN's Scott Burnside.
Richards, 30, hasn't played in the NHL since April 2015.
The NHL Players' Association filed a grievance against the Kings decision to end the deal, which had five years and $22 million on it. Both sides reached a settlement in October.
Richards signed a 12-year, $69 million contract with the Flyers in 2007 but spent four seasons with the Kings starting in 2011. Richards was a key contributor on the Kings' two Stanley Cup championship teams.
He has 179 goals and 303 assists in 710 regular-season games. He won two Stanley Cups with the Kings.
Information from The Associated Press was used in this report.