Bish-Jones has been with Woolworths for six years and will remain in his job for three more months while the search for a successor gets under way.
Woolworths chairman Richard North said: "It's been agreed by the board and Trevor that this is an appropriate time for him to stand down."
He added that headhunters have been appointed, but that no candidates had been identified yet.
Kaupthing analyst Matthew McEachran said: "The search may endeavour to find a CEO with more aggressive turnaround capabilities or with new ideas for the group structure."
Woolworths revealed relatively flat trading this morning when it announced that total group sales were down 1.9 per cent for the 19 weeks to June 14. The retail arm of the business recorded a like-for-like fall of 2.2 per cent.
North said: "Like-for-like sales within Woolworths Retail were broadly in line with our internal expectations - in part reflecting the fact that during this period last year we were actively promoting sales of higher ticket electrical items."
Woolworth also unveiled the disposal of four London stores to Waitrose for£25.5 million.
Sales at 2 Entertain, the Woolworths' joint venture with BBC Worldwide soared, up 29.8 per cent against last year. No update on a possible sale of the stake was provided.
North said that Woolworths remains "cautious" about the consumer economy and that there would be a focus on cash generation and cost control.