The new agency, called Coulson Chappell, is billed as offering "discreet, strategic communication and corporate advice, from a unique perspective, to leaders, companies and organisations in sport and other industries". The agency will also provide communication services including speech writing and media training, it said in a statement.
Coulson left Downing Street five years ago following the backlash over the News of the World phone-hacking scandal. He was editor of the newspaper between 2003 and 2007.
In 2014 Coulson was convicted on phone-hacking charges and received an 18-month jail sentence. Last June he was cleared of perjury in relation to evidence he gave during the trial of former MSP Tommy Sheridan.
Chappell has worked in the sports industry for 20 years. He is the founder and CEO of Pitch, the UK-based sports PR and marketing company.
Coulson Chappell is to operate separately to Pitch, "although synergies between the two companies will be sought", the agency said.
Coulson said: "I’ve always wanted to establish and grow my own company and in Henry I have the perfect business partner. From our combined experience Coulson Chappell can offer a unique perspective to clients looking for clear, discreet and effective strategic advice."
Chappell said: "With Andy’s extensive experience across media and politics, and a growing demand from CEOs, companies and organisations for strategic corporate and communications advice, we feel there is a real opportunity to establish a new agency in the marketplace."