The deal marks the end of a frantic auction which was sparked last month when Mr Barbour, who will be 65 in July, announced his intention to step down and sell his 42.4 per cent stake in the company.
Mr Barbour founded the company with his brother in 1957 after completing his national service and a two-year spell working as an travelling salesman for Encyclopedia Britannica. A former director, David Davenport, who retired five years ago, is set to receive pounds 4.3m for his 8 per cent stake.
Havas won the auction despite intense competition from rival UK companies including Emap, the magazines group, and Lord Hollick's United News & Media. The French group, which is a subsidiary of the media and utilities giant Vivendi, is offering 305p per share in cash for Barbour, valuing it at pounds 53m. Shares in Barbour, which have been buoyed by takeover speculation in recent weeks, dropped 25p to 300p.
Brian Griffin, Barbour's chairman, said Mr Barbour and the rest of the board had favoured Havas' bid because it planned to leave the company intact.