Balfour Beatty pulled out of the battle for Mowlem after it emerged it would have needed to put in a bid worth around £350M to have any chance of eclipsing Carillion's offer.
Amec remains the biggest earner, turning over £4.8bn.
Balfour Beatty said the low price reflected a £20M pension deficit it would take on from Birse. It also said that the new acquisition was part of plans to grow further.
'We do have cash in the bank. We want to grow the business. We are always looking,' said head of corporate communications Tim Sharp.
'We told the analysts in March that we were looking to generate growth through further expansion of our private finance operation, through offering better professional services, and through becoming the market leader in civil engineering and building.
'This is dead centre of number three.'
For the year ended 30 April 2005, Birse made a profit before tax and exceptional items of £2.8M on a turnover of £340.5M.
The company is now working at record levels, with major highways projects for local authorities, a major coastal defence scheme in Blackpool and two five-year frameworks for Nework Rail all underway.
But managing director Martin Budden said the choice was to team up with a bigger firm or be left behind. 'You have got to align with what's happening in the marketplace.
'Jobs are getting bigger and the bigger jobs tend to go to bigger organisations,' said Budden.
'The average size of our projects has increased from £5-10M to £15-25M, but the next league is £50M upwards.
'Our biggest job at the moment is in the £50-100M bracket, but we have only got one of those. We see more projects coming in that range.'
If approved by shareholders the takeover is likely to complete within 30 days. Balfour Beatty said it was likely to retain the Birse brand for the foreseeable future.