The rethink follows allegations that Alastair Campbell, the director of communications and strategy at Downing Street, had taken control of government advertising because Fisher reported directly to him.
The expanded role was handed to Fisher in February to ensure the proper co-ordination of campaigns by different Whitehall departments. But the move was attacked by the Tories and Liberal Democrats as further evidence of the "politicisation" of government ads by Labour.
Bishop's appointment, revealed in Campaign last week, was confirmed on Wednesday by the Cabinet Office. Government sources said he would report to Sir David Omand, the Permanent Secretary at the Cabinet Office, and Douglas Alexander, the minister responsible for COI.
Bishop, 49, the former chairman of Saatchi & Saatchi International, said: "I am very pleased to be joining COI. This is the most challenging job in communications, handling the most important campaigns around. I am looking forward to joining an excellent team."
- Newsmaker, p17.