Thomson said: "I've always wanted to run my own company and after three-and-a-half years at Air Miles, now is the right time to move on."
The news comes three months after the former Grey London chief executive Garry Lace was linked with Thomson and a loyalty venture in an e-mail said by Lace to be a hoax (Campaign, 13 February). It claimed that Lace had quit the agency to set up a loyalty programme with Thomson and others.
At the time, the claims were denied by Lace. Separately, Lace left the agency in March.
A BA spokeswoman confirmed the departures and that Thomson was preparing to set up his own venture. However, she was unable to comment on whether Lace was involved in the MBO.
Thomson and Wooldridge will leave at the end of May.
Lace and Thomson refused to comment.