Cratus Communications is a five-year-old public affairs agency that advises companies and charities on dealing with local government.
Cockell served as the Conservative leader of the Royal Borough of Kensington and Chelsea for 13 years between 2000 to 2013.
He has been chairman of the Local Government Association, a role he is stepping down from, for three years, and is the chairman of local government-focused think-tank Localis.
He will replace James McKechnie, who is becoming chairman of Cratus Group, which owns Cratus Communications, Middlemarch Communications and Rubber Duckiee.
Cockell said: "Cratus knows elected members need to lead the revolution in local public services that is happening across the country and that the public and private sectors need to better understand and learn from each other's strengths."
Cratus has also appointed two non-executive directors, Conservative MP for Bromley and Chislehurst Bob Neill and former MD of John Laing integrated services Tim Grier. John Laing is an asset management company that works on privately financed public sector infrastructure projects.
Grier said: "I look forward to supporting the growth and development of the company as it continues to optimise efficiency and value throughout public service activities in the UK."
Nick Kilby, CEO of Cratus, said Cockell, Neill and Grier "bring extensive experience and offer an unrivalled understanding of local public services, which will further strengthen Cratus’ position in supporting innovation in these sectors".
Cockell, Neill and Grier will start at Cratus on 14 July.