The Millers have admitted in a statement that they are 'shocked and disappointed' by Jackett's decision to resign just 39 days after he was appointed on a three-year deal.
According to PA reporter Jonathan Veal, Jackett offered his resignation after this morning's board meeting, in which the club's January transfer budget was discussed.
The 54-year-old did not win any of the five games that he was in charge of having drawn one and lost four - the most recent of which ended in a 2-1 defeat to Leeds United.
A statement via Rotherham's official website read: "Following the game against Leeds United at the weekend, Kenny Jackett tendered his resignation and accordingly, his employment with the club has terminated with immediate effect.
"Kenny's resignation came as a shock to the club and is disappointing. The club will now focus on making appropriate arrangements for the first team."
Paul Warne will take charge of the first team until the club appoint a permanent replacement.