The versatile full-back, who can also play in midfield, has been brought in by Eagles boss Ian Holloway to replace the released David Wright.
Richards is expected to be available for Wednesday's clash against Huddersfield, subject to the deal being approved by the Football League.
"Swansea were happy to let me go out on loan and when I spoke to the gaffer here, it was a great opportunity for me," said Richards.
"It's a brilliant club to be coming into, sitting in the top six of the Championship. As a player you want to be fighting for a place in the Premier League and hopefully I can play my part in the club getting there."
Richards has been restricted to just four appearances for the Swans this season, three in the Capital One Cup and one in the FA Cup third-round replay defeat to Arsenal.
He has not featured in a Premier League game since December 2011, although he did win his first cap for Wales in their 2-0 defeat to Mexico last May.