The 67-year-old succeeds Paul Trollope who was sacked on Tuesday after a disappointing start to the season which has brought just two wins from 12 matches in all competitions.
Warnock will work alongside Kevin Blackwell and Ronnie Jepson, named as assistant manager and first team coach respectively, while existing staff members James Rowberry, Martyn Margetson and Lee Southernwood will continue as part of the back-room team
However, Trollope's assistant Lennie Lawrence and conditioning coach Ryland Morgan have departed.
Cardiff confirmed the appointment via their official website on Wednesday morning, a statement read: "Cardiff City Football Club is delighted to announce the appointment of Neil Warnock as first team manager.
"Kevin Blackwell and Ronnie Jepson will join Neil as assistant manager and first team coach respectively, while existing staff members James Rowberry, Martyn Margetson and Lee Southernwood will continue as part of Neil's immediate back-room team."
Warnock steered Rotherham away from relegation from the Championship last season
After joining the Millers in February he guided them to safety, nine points clear of the drop
He joins Cardiff with a similar remit after a 2-0 defeat at Burton on Saturday left the Bluebirds second from bottom of the table.
Cardiff is Warnock's 14th managerial job and he spoke of his desire to win a record-breaking eighth promotion when he turned down the chance to remain at Rotherham at the end of last season.
Warnock's first game in charge sees Cardiff host rivals Bristol City on October 14 when the Championship campaign resumes following the international break.
Source : PA