Both Glasgow sides have reached the group stages of the competition and will play six matches each on Thursday nights during the autumn.
Their league games scheduled for Saturdays will now be moved to Sundays to give them more time to recover.
The new dates for the fixtures are:
Sunday September 22: Celtic v Kilmarnock, kick-off TBC
Sunday October 6: Rangers v Hamilton Academical, 3.00pm
Sunday October 27: Rangers v Motherwell, 3.00pm
Sunday November 10: Celtic v Motherwell, 3.00pm
Sunday November 10: Livingston v Rangers, 3.00pm
Sunday December 1: Rangers v Hearts, 3.00pm
Sunday December 1: Ross County v Celtic, kick-off 3.00pm
Sunday December 15: Celtic v Hibernian, 3.00pm
Sunday December 15: Motherwell v Rangers, 3.00pm