O'Shea, 59, acclaimed as one of the best copywriters of his generation, will leave Miles Calcraft Briginshaw Duffy when his current commitments are complete.
Hoggins, O'Shea's art director, whose professional relationship with him spans more than 20 years and five agencies, will remain at Miles Calcraft, but with a new partner, Paul Hodgkinson, who joined the agency this week.
Hodgkinson was previously at M&C Saatchi for almost ten years, where his credits include British Airways and NatWest. He will replace O'Shea on the Waitrose business.
O'Shea said: "The time feels right to move on. When you do something that's so all-absorbing, you don't have time for other things.
"I hope to continue doing some consultancy work, but I also want to finish my novel and take flying lessons."
Paul Briginshaw, the MCBD creative partner, said Waitrose executives had seen Hodgkinson's work and supported his appointment. "It's been a smooth and seamless change," he said.
Hoggins and O'Shea have been associated with the Waitrose account since they first started working on it at the then Banks Hoggins O'Shea/FCB in 1997.
The business moved with them when they established their own agency, HOW, in the summer of 2003, and stayed there when HOW merged with MCBD in November last year.
O'Shea and Hoggins first worked together at Lowe Howard-Spink in the early 80s, where they became joint creative directors. One of their most famous executions was a print ad for Stella Artois featuring the line: "My shout, he whispered."
O'Shea's considerable haul of awards includes two gold, two silver Cannes Lions, a Campaign Press gold, and seven silvers.