Western, which operates bus services in Gloucestershire, Wiltshire, Warwickshire, Oxfordshire and South Wales, was a buyout from the National Bus Company in 1986.
The deal follows the recent purchases by Stagecoach of East Kent Buses and Grimsby Cleethorpes Transport. The three deals bring Stagecoach a combined turnover of pounds 55m.
Brian Souter, chairman, said: 'We are particularly pleased about getting a presence in an area where we have not been previously.'
The group was looking at other opportunities. 'But the important thing is that we have to be comfortable not only about what we are buying but also the price,' he added.
Western, which has about 1,700 employees, made pre-tax profits of pounds 1.9m last year on turnover of pounds 33.9m. Stagecoach is paying with cash, loan notes and new shares.
Stagecoach was floated in April. Its shares were firm at 141p yesterday.