The 28-year-old was fundamental to the Clarets' successful promotion charge in the 2022-23 campaign, and he started each of Burnley's first seven Premier League fixtures in the current term.
However, Roberts has not made a top-flight starting XI since a 3-0 loss to Brentford on October 21, with Vitinho being preferred on the right-hand side of the backline by Vincent Kompany.
With Rennes' Lorenz Assignon and Montpellier HSC's Maxime Esteve also arriving on deadline day to strengthen Kompany's defensive ranks further, Roberts has dropped back down to the Championship for the rest of the campaign.
"I think for me personally, it's a massive opportunity to come and play for such a big club like Leeds United. It's something I couldn't say no to and to hopefully be part of something special come the end of the season is what I am aiming for, and everyone in that dressing room is aiming for," Roberts told LUTV.
"If I can contribute both on and off the pitch in every way possible, hopefully we can all be smiling. I have got plenty of friends here who play here and tell me about what an amazing club it is, it's something that I couldn't turn down. To even get to play a handful of games for this massive club, it will be an absolute privilege."
The Wales international links up with compatriots Daniel James, Ethan Ampadu and Joe Rodon at Elland Road, and the Whites have confirmed that his debut could arrive against Rotherham United on February 10, as he is ineligible for next week's FA Cup fourth-round replay with Plymouth Argyle.