Richards, who can play at full-back and in midfield, has been brought in by Eagles boss Ian Holloway to replace David Wright after he was allowed to leave the club.
The 21-year-old is expected to be available for Palace's next game against Huddersfield on Wednesday.
"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," Richards told the club's official website.
"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."