The 30-year-old Swansea defender and 29-year-old West Brom midfielder have joined the Championship club until January as Neil Warnock looks to lift his side from 18th position
Tate has made just four appearances for Michael Laudrup's men this season, and has been given the chance of playing regular football for Neil Warnock's side, who are languishing in 18th in the table.
And 29-year-old midfielder Thomas has been on the boss' watch list for some time, with Warnock revealing he has tried to sign the player five times.
"[Thomas] is just what I'm looking for and I want him to come here and enjoy himself," he told the club's official website.
"He's direct and positive when he's attacking and fits the bill as just what we want.
"He's a player I've tried to sign five times so it's about time I finally got him."
Tate has made over 250 appearances for the Swans since joining them on a free transfer in 2004, and Warnock praised the player's leadership qualities.
"[Tate] is a lad who I've always enjoyed playing against," he told reporters.
"He is a leader and I felt these last few weeks we've lacked leaders. It's great to have him in. "
Leeds are seven points off the foot of the table but are also eight away from the play-offs, and Warnock feels the move will be beneficial for both Tate and his club.
"We're short on bodies in there, so he'll play on Saturday [versus Crystal Palace]," he added. "He's got a great attitude - it's a super club for him."