The 50-year-old Yorkshireman makes his return to the game following his exit from Elland Road in the summer following a bitter fall-out with United owner Massimo Cellino.
Redfearn had also been in the running for the vacant post at the Millers’ South Yorkshire neighbours Doncaster Rovers, but was thought to be keen to remain in the Championship.
Redfearn was among a handful of candidates interviewed for the Millers post this week, with second interviews understood to have taken place with those who had impressed today.
Hibernian head coach Alan Stubbs was also believed to have been firmly in the running for the post to replace Evans,who left the club on September 28.
Other linked included Walsall chief Dean Smith, with the Saddlers rejecting an approach for the Millers to speak to him earlier this week.
But Redfearn has consistently remained the favourite for the job.
Redfearn, who enjoyed a successful playing career which included spells at Barnsley, Bradford City and Doncaster Rovers, took over as full-time Leeds’ head coach on November 1 after three previous stints as caretaker boss before returning to run the club’s academy.
Redfearn makes his return with the Millers to Elland Road on November 21.