It will also net British Bus founder Dawson Williams an estimated pounds 10m. The company had been planning a flotation when details of a Serious Fraud Office enquiry into Mr Williams emerged last year.
Cowie will fund the deal through 1 for 3 rights issue priced at 355p, raising pounds 186m. Cowie will also take on British Bus' pounds 100m of debt.
British Bus is strong in the Midlands, Yorkshire and the North West, while Cowie's beat is in north and south London.
Cowie chief executive Gordon Hodgson described the deal as: "The last remaining opportunity for a strategic acquisition of an independent business in the UK bus industry." He said the company was still looking for other deals.
Last year, British Bus made operating profits of pounds 34m on sales of pounds 261m. Cowie shares closed 3p higher at 409p.