Cox, who over a long career has created campaigns for Barclaycard, Sainsbury's John Smith's and Walkers Crisps, is stepping down after a period of ill- health. He will continue to work for the agency on a project basis.
The news, which calls time on a five-year relationship, addresses the weaknesses in AMV's senior creative line-up, which is stretched following the departure of Nick Worthington to Publicis Mojo in September.
Meanwhile, Peter Souter, the agency's executive creative director, is to partner Paul Brazier, Worthington's former art director. Souter will continue working a four-day week.
Belford and Roberts will report to Souter and Brazier. The agency's eight "editors" will sit between Belford and Roberts and the rest of the agency's creative teams.
Souter said: "I am looking to replace Nick Worthington and Tony Cox. But at the moment it's much more about giving Nigel and Paul the opportunity to do better work. They have fantastic judgment and an unbelievable work ethic.
"Losing Tony is obviously terrible and something not many agencies could stand and pretend is nothing."
The appointment of Belford and Roberts as the creative directors is a controversial one. The team was stripped of a number of Campaign Press Awards in 2002, when it emerged that their entries for The Observer, COI Communications and The Samaritans were doctored versions of the ads that actually ran.
They joined AMV in 2002, moving from Ogilvy & Mather, where they were the creative directors. The pair have effectively been operating as creative directors since Cox fell ill last year.
They will now be charged with raising creative standards at the agency and assuming responsibility for recruitment.