Mellish set up the consumer agency at the start of 2011. Current clients include Perrier, Rowntree's, Miele and bourbon brand Woodford Reserve, and it placed 131st in the 2017 PRWeek UK Top 150 Agencies. It has 20 staff.
The firm's founder previously owned a third of the agency, with the remaining stake being held by Shoreditch-based Captivate Group, chaired by Paul Seligman. Mellish's stake has now been sold back to Captivate for an undisclosed sum.
New MD Vyvyan-Robinson has spent the previous six-and-a-half years at Freuds as an associate director, before which she worked alongside Mellish at the agency Phipps. At Freuds she played a leading role on its KFC account, helping it retain the brief earlier this year, and previously on its Asda account.
In May, Stir's client services director Jo Seymour-Taylor left the business after more than five years. She was paid £18,400 for selling her six per cent stake back to the business, Companies House documents show.
Mellish told PRWeek she was going to start a course in architectural interior design next year with the intention of a permanent career change.
She said: "If I could have chosen anyone, it would have been Jo Vyvyan-Robinson and I don't think I'd have felt as calm about handing over my baby to anyone else. There's no-one that I feel is better placed to help Stir realise its potential."