Rivett previously ran his own brand and digital comms consultancy, Paratus Communications, for eight years, before it was acquired by Next 15 Group.
Paratus merged with Lexis in 2012 and Rivett became head of consumer & sport.
Throughout his career he has delivered campaigns for global brands including Costa Coffee, Coca-Cola, Vodafone, Harley-Davidson, Smirnoff Vodka, Audi, Ford, Levi Strauss, Goodyear, Motorola and adidas.
Before starting Paratus, Rivett was deputy chief executive of Hill & Knowlton London and ran its EMEA marcoms network.
He is replacing Will Powell.
David Wilson, Bell Pottinger group managing director, said: "John has an unquenchable passion for consumer engagement and an ability to really understand clients to deliver the appropriate creative and strategic direction of work. It is this insight, approach and energy that will ensure we take our consumer proposition forward within our integrated communications offer at Bell Pottinger."
Rivett added: "I am excited to have joined Bell Pottinger to develop a consumer proposition that will really connect brands and businesses with their customers and other key audiences."