The start-up, called Who Wot Why, is based in Shoreditch, East London, and aims to "make brands famous" by creating work that is talked about in the pub by people outside the industry, Walker said.
The trio previously worked together at Wieden & Kennedy on award-winning work for Honda, including "Cog" and "Grrr". "Grrr" won the Film Grand Prix at Cannes in 2005.
Gooden and Walker left Crispin Porter & Bogusky in March last year after the shop lost its two biggest clients, Milka and Paddy Power. They joined Crispin Porter & Bogusky from BMB in 2011.
Thompson, who left Dare in 2014 after 14 months, said setting up as three creatives – rather than the traditional trio of account handler, planner and creative – was a "conscious decision".
He added: "We value the skills of account handling and there are some great ones out there who we want to hire but, having spoken to clients, we realise first and foremost they want to go straight to the source of the creatively strategic ideas.
"They prefer to get as close as possible to the work that is going to change their business for the better. We believe there is a new way of doing things that is more streamlined.
"When all’s said and done, it’s the ideas that count."