VCCP's Adrian Coleman and Matthew Vandrau of Chime Sports Marketing will take over his duties as co-chief executives in January.
Satterthwaite has more than quadrupled operating income and headcount since he became chief executive in 2003 and turned Chime from a public relations business into an international sport, entertainment and communications group.
He oversaw the sale of a majority stake to Providence Equity Partners in 2015 in a £374m deal that has helped to fund further expansion.
Satterthwaite, who is 61, said: "This is the right time for the next generation to take control. It is two years since the buy-out and I get a real sense that the group is working closer together and I want to go off and do new things."
He pointed to global wins of Cadbury and HSBC this year as proof the expansion plan is working. HSBC gave CSM its sponsorship activation business earlier this year.
Coleman will retain his role as chief executive of VCCP and Vandrau will stay as chief executive of Chime Sports Marketing in addition to their co-chief executive group roles.
Chime has made a string of other appointments to its management team.
Joanne Parker, chief executive of Chime Specialist Group, which includes its pharmaceuticals division, has been named chief operating officer of Chime.
Stephanie Brimmacombe, chief marketing officer of VCCP, has been appointed group managing director of Chime.
Charles Vallance, chairman of VCCP, becomes head of strategy for Chime.
Satterthwaite said having co-chief executives, rather than just one leader, can work well. "I'm a big believer in it," he said, noting Coleman and Vallance have jointly run VCCP.
Chime's board wants Coleman and Vandrau to drive more integration as co-chief executivess. VCCP and CSM have only a handful of shared clients, including Vitality and Old Mutual.
Satterthwaite said: "I have every confidence that both Adrian and Matthew will be strong leaders of the company, supported by Stephanie Brimacombe, Jo Parker and a highly talented overall management team."
He will remain on the Chime board and become a non-executive director alongside the chairman, Paul Walsh, the former chief executive of Diageo.
Satterthwaite began his career as a graduate trainee at Heinz and is a former chairman of the Roundhouse arts venue in London's Chalk Farm.
He has a reputation for being self-effacing and genial but he has shown mettle at Chime, facing down WPP, a minority shareholder, in the past and dealing with big personalities such as Lord Bell, the former chairman of Chime, and Lord Coe, who continues to chair CSM.
Coleman, who has worked with Satterthwaite for over 25 years, said: "He's done an absolutely fantastic job for the company. He's turned it from a small plc into a decent-sized business."
Chime's most recent accounts show it had operating income of £246m and 2,200 staff in 2016 compared to operating income of £54m and 585 staff in 2003. Headcount has risen to about 2,500 this year.
Notable acquisitions have included VCCP in 2005, Coe's Complete Leisure Group in 2012, motor-racing business JMI in 2013 and and Adconnection in 2015.
Andrew Tisdale, managing director of Providence, said it was "incredibly grateful to Chris for his leadership".
Satterthwaite said the private equity firm has "been very supportive", improved the management of the agencies through "the rigour of financial control", and "allowed us to grow in a way that we’d never have been able to do internationally" if Chime were still on the stock market.
He played down suggestions that Providence might want to sell in the near future. "Now that we're starting to win global accounts, we can grow exponentially over the next three years," he said.
Satterthwaite is bullish about the prospects for sports marketing, in particular, and claims English Premier League football is bigger than Facebook because it reaches three-quarters of the world's population.
Looking back on his 40-year career, Satterthwaite said: "The big change is the communication has become distribution.
"When I trained at Heinz, you spent a lot of time distributing product in the right aisles and shops. Now you can communicate something and in two clicks you're paying for it."
This article first appeared in PRWeek sister title Campaign