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.”
Stoke could face a battle to keep Xherdan Shaqiri as reports have claimed Mark Hughes wants him at Southampton next season.
Bayern Munich have entered the race to Emre Can, who continues to talk up a move away from Liverpool this summer.