The 35-year-old takes up the position on a two-and-half-year deal which will run until the summer of 2023. The club say Rooney has "elected to call time on his illustrious playing career" to fully focus on his job.
Rooney stepped up to lead Derby’s coaching team towards the end of November after former manager Phillip Cocu was sacked by the club.
He oversaw nine matches, three of which the club one, four of which they drew.
Rooney’s first game as Derby’s new permanent manager will be Saturday’s fixture at home against Rotherham United.