Sir Win Bischoff, 72, will be paid £120,000 a year for two days work a week at the FRC from May. The council recently launched a probe into the Co-operative Bank's accounts.
Sir Win's appointment, for a three-year term, was announced by Business Secretary Vince Cable. A spokesman for the department denied there was a conflict of interest.
Lord Levene suggested to the Treasury Select Committee this week the Lloyds branch sale to Co-op was "swayed by political considerations". The deal collapsed after a £1.5 billion black hole was found in the mutual's finances.