Their departures will leave a large gap at the agency, as the newly installed chairman tries to rebuild O&M's standing in the London market.
The agency is looking to replace the pair very quickly. An O&M statement said arrangements for the management succession will be in place by October.
The duo, who will remain at the agency until December to ensure a smooth management change-over, say they are planning to set up their own business in a year's time.
They first started working together at DDB in 1995 and joined O&M in June 2004. Roberts has worked on clients such as Pilsner Urquell and Slimfast, while Cunningham had a wider client remit.
Roberts said: "We have worked together for a long time now. We have always talked about setting up a business together and this seems like the perfect time."
Cunningham added: "We will spend a few months getting the positioning right and then the business, which will be in the marketing realm, will be opened up sometime towards the end of next year."
Paul Jackson, the chief executive of O&M, said: "Both Jane and Philippa have made a valuable contribution to the agency during their time here and leave with our thanks and best wishes."