The 28-year-old joined the club ahead of Saturday's Elland Road clash with Swansea City.
The Welsh international went straight into the squad for the game against the Swans, following a foot injury sustained by Kasper Schmeichel.
Simon Grayson said: "Kasper picked up a foot injury a couple of weeks ago and we are assessing him as we go. We have a lot of games coming up and I'm delighted that Jason has agreed to come in."