The 49-year-old who has won promotion to the Sky Bet Championship three times with Rotherham, emerged as favourite to succeed Wayne Rooney earlier in the week after the Rams began the season under interim boss Liam Rosenior.
Warne had been in charge of the Millers since 2016 and oversaw three promotions to the Championship and an EFL Cup win while working under significant financial restraints.
He guided Rotherham to eighth place in the Championship after nine games this season - their best start in the second tier since the 1960s.
Derby said in a statement: "Derby County Football Club are delighted to announce the appointment of Paul Warne as head coach.
"Warne has joined the club with immediate effect on a contract until the summer of 2026.
"As was made clear in the summer, the board intended to take a period of time evaluating every aspect of the club and having done that, we believe Paul's track record of success at this level fits perfectly into our long-term strategy."
Caretaker boss Rosenior had been backed by Derby's new owners Clowes Developments to make the job his own after Rooney resigned in June.
But the 38-year-old, who had been Rooney's assistant, has been relieved of his duties and it is not clear whether he will remain at Pride Park.
Derby confirmed Warne's Rotherham coaching staff - assistant head coach Richie Barker, first team coach Matt Hamshaw and first team goalkeeper coach Andy Warrington - have joined him at the club.
The Rams said: "Paul's arrival means the end of Liam Rosenior's tenure as interim manager and, on behalf of everyone at Pride Park Stadium, we would like to thank Liam for all his efforts during an incredibly difficult period and in helping to stabilise the club under new ownership."
Warne, who spent six seasons at Rotherham, will take charge of his first game for Derby at Cambridge on October 1 after the international break.
Derby added: "We would also like to thank Rotherham United and their chairman Tony Stewart for all their assistance throughout this process."
Rotherham said: "While of course we are disappointed to see Paul and his staff depart, they do so with our very best wishes and thanks for their commitment to their roles here with Rotherham United.
"Their departure now provides the club with an exciting opportunity to bring in a new team of coaching staff with a fresh perspective and build on our excellent start to the 2022/23 Sky Bet Championship season."