Moore and assistant Jimmy Mullen both leave the Millers by mutual consent after 18 months in charge after the 5-0 defeat to Chesterfield last Friday.
News first broke on this website on Monday afternoon, with BBC sources later confirming events with a statement on the clubs official website at 1pm on Tuesday.
The club are five points off an automatic promotion place with nine League Two games to go this season.
First team coaches and senior players Paul Warne, Andy Liddell and goalkeeping coach Andy Dibble step in to take temporary charge.
Source: BBC Sport