The 26-year-old midfielder has signed "an initial one-year deal", with Ray McKinnon expressing delight at his first signing as manager at Tannadice.
"He is exactly the type of player we need going into this season," he said.
"Not only is he the right age and a good footballer, but he is a ball winner who is strong in the tackle and will protect our central defenders."
Murdoch had joined County last summer after his departure from Fleetwood Town.
But half of his 34 appearances came as a substitute and he followed fellow midfielder Rocco Quinn out of the Scottish Premiership club.
Murdoch, who began his career with Falkirk and had a loan spell with Northampton Town before joining Fleetwood in 2013, told United's website: "I'm delighted to be joining Dundee United - it was an easy decision to make.
"It's a massive club and I want to help them get back to the Premiership, where they should be."
Following United's relegation from the top flight, 13 players have exited Tannadice along with manager Mixu Paatelainen and his backroom staff.
While Murdoch and Quinn have exited County, manager Jim McIntyre has already recruited three defenders and a goalkeeper, Aaron McCarey from Wolves, this summer.
Christopher Routis has arrived from Bradford City, Kenny van der Weg from Breda and Erik Cikos from Slovan Bratislava.
Stewart Murdoch has signed for Dundee United the day after his contract was terminated a year early by Ross County.