Derbyshire, who has hosted a mid-morning show for a decade and prior to that hosted the breakfast slot, said she was moving to take up an unnamed "brilliant opportunity".
The station says it is the "biggest shake-up to its daytime schedule in years". It will kick in from October.
Afternoon presenter Bacon is leaving after seven years and among his future projects will be a BBC1 series hunting for amateur painters.
Fogarty, a former breakfast co-host who now presents the lunchtime show, said she is "exploring a number of opportunities".