Burkitt will leave the agency that carries his name at the end of October.
The agency name will not be changed after his departure.
The former Advertising Standard Association council member and chairman of the IPA's advertising controls group, will now have to relinquish his position as a council member of both the IPA and the Advertising Association.
Jo Hoare will step up into the role of agency chairman, combining it with his current responsibility as the managing director. Rodwell, the agency's vice-chairman, is passing his client handling role to Julian Calderara, the deputy managing director.
Burkitt said: "I have completed the job which I agreed to do here for DDB of creating one of London's few truly integrated advertising agencies. We have a strong team here now in all the key disciplines, and we've had some significant successes in the past two years."
Burkitt sold his independent agency, Court Burkitt, to Omnicom and merged it with Griffin Bacal in July 2000.
Burkitt will be having a short break before taking up the mantle as an independent consultant.
He added: "I want to be able to advise clients about the whole advertising process from a position where I have no vested interest in selling any specific service. I also plan to write my own guide for clients on how to get the best out of agencies."
Burkitt started his career at Collett Dickenson Pearce in 1972. He founded Burkitt Weinreich Bryant in 1986, at which time his partnership with Rodwell began.
Rodwell, who spent 13 years of his early career at BMP, will now be taking a short break. After this he will be following interests both inside and outside advertising, including his role as the chairman of the London Community Cricket Association.
Burkitt DDB's most high-profile work in recent times has been its idents for T&T soft drinks, which ran in the ad breaks for Pop Stars.