The Scottish international made his 50th league appearance for the Reds in the 1-1 draw at Charlton at the beginning of the month but was just starting to become squeezed out of Freedman’s plans for the remainder of the campaign.
A solid Championship performer since his move from Glasgow Rangers to Cardiff City in January 2009, 32-year-old Burke will now look to help Rotherham beat the drop into League One.
His departure means that Freedman can bring in a new face to his squad under the terms of the FFP restrictions currently placed on the Nottingham Forest manager.