Stubbings, a former managing director of Bates, who took control of the group's below-the-line operations in September 2000, has transferred to a consultancy role while "looking at other career options".
Stubbings is seen as part of the Bates "old guard" and has found his responsibilities increasingly taken over by Dennis Kerslake, the managing director of 141, the Bates integrated operation.
Toby Hoare, the group chief executive of Bates, said: "John has been a fantastic servant of this company but we have agreed that now is the time he should do something different. It's perfectly amicable."
His departure comes as news emerges that Carole Butler, Bates' board account director on Woolworths, which is currently under review, has been moved off the account.
Her exit from the account team comes as Bates prepares to defend its 17-year tenure on the business in a four-way pitch. Butler is talking to the agency about her future.
Bates said that the decision to switch Butler away from the Woolworths account had been agreed before the review and was not a direct result of it.
She is being replaced by Sara Bennison, a former senior executive on the Procter & Gamble business at D'Arcy. Hoare said that Bennison would be retained irrespective of the result of the Woolworths review.
Bates has made a number of personnel changes on the Woolworths account team in response to client disquiet. The agency is also believed to be closely scrutinising senior staff salaries as part of efforts to keep costs under control.
"Carole is looking at a number of entrepreneurial business opportunities and I'm talking to her to see if we might be a partner in one of those," Hoare said.