The experienced winger will spend the rest of the season with the League One side.
Murphy, who is 30 years old, has seen his time at Ibrox stricken by injury and is hoping to get some game time under his belt with the Brewers under a former manager in Nigel Clough.
The Scotland international joined Rangers in January 2018 from Brighton and Hove Albion on loan before making the move permanent that summer. He has made 26 appearances for the Glasgow side, scoring twice.
Murphy has previously played for Motherwell and Sheffield United. He was a key player for the Blades and played 122 times for the Yorkshire side and scored 21 goals.
After joining Burton he told their official club website: “The training ground is second to none and it was good to get out there and get a training session in with all the boys. I have worked with Nigel Clough before and had some of my greatest moments as a footballer under him, so it was an easy one to pick coming here.”
“I want to be back enjoying football again. It has been a nightmare time with my knee but I’m now just looking forward to playing again and hopefully helping the boys win on Saturday.”
Clough has said: ” “We can’t quite believe we have got him, but we are absolutely delighted. When we heard he was down to go out on loan we made an enquiry but to get a player from Rangers of Jamie’s quality is brilliant.”
Murphy has been given the number 29 shirt by Burton and is looking forward to getting some games under his belt.