The 31-year-old former Liverpool full-back, also wanted by West Ham boss Sam Allardyce, passed a medical at Thorp Arch on Thursday afternoon and is expected to go straight into the squad for Saturday's home clash with Cardiff.
"I'm absolutely delighted again," said Leeds manager Neil Warnock, who earlier in the day completed a swap deal that saw Steve Morison arrive from Norwich with Luciano Becchio heading in the opposite direction.
Warnock added on the club's official website: "Stephen has the experience I think we need in that position.
"He's a former international who, for whatever reason, has been allowed to leave Aston Villa.
"He's a player I've tried to sign a few times before and I'm pleased he turned down West Ham to come here."
It is understood West Ham were not prepared to offer Warnock a long-term deal.
Warnock, born in Ormskirk, started his career at Liverpool before Blackburn paid £1.5 million for him in January 2007. He joined Villa two years later and made 104 appearances for the Midlands club.
He made 15 appearances for Bolton during a three-month loan spell earlier in the season.
Leeds have also signed striker Mouhamadou Habib Habibou from Belgian club SV Zulte Waregem on loan until the end of the season.
The 25-year-old, who is a Central African Republic international, has joined the Elland Road outfit with a view to making his move permanent in the summer.
Boss Neil Warnock told the club's official website: "He's a player we've had across for a few days and we liked what we saw.
"We had the opportunity to take him on loan and that gives us a chance to have a longer look at him.
"We think he could be an exciting prospect."
Habibou added: "I'm very happy to be here. I know about the background of the club and the expectations around the club and I'm happy to sign and start playing."