Murphy has fallen out of favour at Leeds since Garry Monk took over and has been made to train with the Under-23 side.
The 27-year-old signed for Leeds from Crewe Alexandra in 2013 and has scored seven goals in 103 appearances.
On his move to Burton, Murphy said: “As soon as I found out there was a chance of coming here I really wanted to make it happen.
“It’s a very ambitious club and they’ve proved that in the last few years with the promotions.
"With the manager that’s here I’ve always wanted to try and play for him and hopefully I can help the team do well and finish the season good.”