The 43-year-old former Millers midfielder took over in November after Kenny Jackett's resignation.
They were relegated to League One with seven games of the season left after a home defeat by Fulham on Saturday.
"Paul knows the club inside out. He is a Miller, through and through," chairman Tony Stewart said.
"Paul has greatly impressed the board in a number of areas, in what has been a very difficult situation over the past few months.
"Whilst he has held the title of fitness coach, he has always been much more than that under a succession of managers who have all tapped into his knowledge, motivational skills and coaching ability."
Warne had two spells with the club a player, making a combined total of 263 league appearances, before joining the coaching staff under manager Steve Evans in 2012.
He is the club's fifth manager since Evans left in September 2014 following Neil Redfearn, Neil Warnock, Alan Stubbs and Jackett, who left after just five games.
Warne won three of his first eight league games in charge, but the Millers are now on a run of nine successive defeats after Tuesday's home loss to South Yorkshire rivals Sheffield Wednesday.
BBC Radio Sheffield sport editor Andy Giddings
Paul Warne has seemed to be the board's overwhelming choice for some time.
Warne has overseen the clubs relegation from the championship, but he shouldn't be fully judged until he's allowed to build his own team.
The direction of the season was set long before he succeeded Kenny Jackett. Recruitment, as ever, is key to success, and he'll be aided by the club's plans to improve the infrastructure.
Although no appointment is universally welcomed by supporters, Warne has retained the lion's share of support he's enjoyed as both a player and coach.
Relegated Championship side Rotherham United have appointed interim boss Paul Warne as their manager on a one-year rolling contract.