The move comes after Bish-Jones spent more than six years struggling to put the group back on the road to recovery.
Richard North, the chairman of , said the board had decided that now was an appropriate time for the company to find new leadership, but insisted that the parting was on friendly terms.
The decision comes hot on the heels of disappointing trading figures from Woolworths, in which like-for-like sales were down 2.2% for the first 19 weeks of the year to June 14. Total sales were down 1.9% compared with last year.
North said: "Trevor has been a tireless chief executive for almost all the time that Woolworths has been a separate listed company.
"I've been very pleased to have him as my chief executive and he has been responsible for some very significant things, including the complete reinvention of Entertainment UK [the company's DVD and music distribution business] and the refinancing of the business, which was not easy to pull off in last year's markets.
"It has been agreed between the board and Trevor that this is an appropriate time to seek new leadership for the business."
Bish-Jones appeared to be reviving Woolworths' fortunes earlier this year, when the retailer bounced back into the black with a profit of just £3.4m against a loss of £12.9m the year before.
The company's advertising, created by Bartle Bogle Hegarty, features two puppets called 'Woolie and Worth'.
The TV campaigns, which focus on price cuts, have featured a slew of celebrities in the last couple of years including 'X-Factor' winner Shane Ward and Hollywood action star Jackie Chan.
Bish-Jones will stay on at the company for three months while the search for a replacement begins. Both internal and external candidates will be considered, the company said.
Shares in Woolworths fell 0.63p, 6.4%, this morning to 9.15p.