Wilder has been out of work since leaving Sheffield United in March.
Wilder had been out of work since leaving the Bramall Lane, where he had been in charge for five years, in March.
The 54-year-old guided the South Yorkshire outfit from the third tier to the top flight but they struggled last season and were bottom of the Premier League when he made way.
Wilder, who began his managerial career with non-League Alfreton Town 20 years ago, has also had spells at Halifax, Oxford and Northampton.
He took Oxford back into the League in 2010 and also won League Two with Northampton in 2016. He will be joined at the Riverside Stadium by his long-time assistant Alan Knill.
A statement on the Boro website read: “The club are delighted to confirm the appointment of Chris Wilder as our new manager.”
Boro are 14th in the Championship and have won just six games this term.
Warnock, 72, had been at the helm since the summer of 2020. The side finished 10th last season.