The versatile 22-year-old, who can play at either full-back position or in midfield, will go straight into Mark Robins' squad for Saturday's home derby against Doncaster.
Town boss Robins has moved quickly to draft in cover for right-back Jack Hunt, who joined Crystal Palace for a reported £2million fee on transfer deadline day.
"With Jack Hunt's departure and the recent injury that Calum Woods has suffered, we were looking to increase our options in that area of the pitch and Jazz is exactly the type of player we have here at the club," Robins told the club's official website.
"He is young, but has good experience of the Championship with Swansea and last season's loan at Crystal Palace, and now he's hungry for more.
"Swansea play good passing football and he fits the mould when it comes to playing in our side.
"He has a lot of quality both technically and physically and we're delighted to have him at the club."
Richards is a product of the Swansea academy and made his debut for the Welsh club as an 18-year-old against Middlesbrough in 2009.
He has made over 35 first-team appearances for Swansea and featured on 11 occasions for Crystal Palace while on loan there at the back end of last season.
The Swansea-born defender made his senior debut for Wales in a 2-0 defeat to Mexico in New Jersey in May 2012.