Murphy has made 111 appearances for Leeds since arriving from Crewe for a fee of about £1m in July 2013.
But the 27-year-old has played in just one first-team game this season, in a 1-0 EFL Cup win at Luton in August.
"Burton are a very ambitious club and they've proved that in the last few years," he told the club website.
"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."
Find all the latest football transfers on our dedicated page or visit our Premier League tracker here.
Burton Albion have signed midfielder Luke Murphy on loan from Championship rivals Leeds United until the end of the season.