Bishop, who left Saatchis in January when its senior management was slimmed down after 16 years with the agency in London and New York, takes over from Carol Fisher. Fisher quit the high-profile job at the Government's advertising and marketing department in July.
Bishop was formally offered the job at a meeting on Tuesday with Douglas Alexander, the Cabinet Office minister responsible for COI. He emerged as the preferred candidate of an appointments panel, which interviewed four candidates a week earlier.
It is believed that Bishop was approached by Whitehead Mann, the headhunter called in by the Government to find a heavyweight with private sector experience.
Although Fisher clashed with some COI clients in Whitehall, ministers believe that she improved COI's performance. One ministerial source said: "We are delighted we have found someone with a good understanding of strategic communications and an understanding of the client side of marketing."
To avoid a wrangle over renewing his contract, Bishop has been appointed on a permanent basis instead of the three-year deal given to Fisher. He will inherit a government advertising and marketing budget of about £300 million a year and 370 staff.
The other candidates on the all-male shortlist included Simon MacDowall, the director of communications at the Department of Work and Pensions, the only "internal" Whitehall candidate. Raoul Pinnell, the vice-president of global brands and communications at Shell International, withdrew from the race after making the shortlist and was not interviewed.
Bishop joined Hobson Bates as a graduate trainee in 1974, moved to Milton Sharam Gottlieb as a founder partner in 1978 and was an account director at Foote Cone & Belding from 1981 to 1983, when he became a board account director and new-business director at Ted Bates.
He joined Saatchis as a board director in 1985 and was widely credited with revamping Saatchis' New York office after moving there in 1994.
Although he returned to Charlotte Street in 1997 to become the chairman, he stood down in 1998 when he was shifted to an international role as part of a top-level shake-up.
Peter Buchanan, Fisher's deputy and currently the acting COI chief executive, did not apply for the top post. He will stay on as the deputy chief executive.