Mowlem shareholders have voted in favour of a £313m takeover by Carillion.
Mowlem said on Monday it had secured more than 99% of shareholder support at a court meeting and extraordinary general meeting.
The deal, which represents an offer of 220p a share, will create a £4bn-turnover company in the same league as Balfour Beatty, and has already prompted market speculation about further consolidation among contractors.
Carillion structured the recommended offer as a "scheme of arrangement", which means that it is required to secure at least 75% of shareholder support if the bid is to succeed.
Mowlem first announced that it had received a preliminary approach at the end of October last year.
Early in December, Carillion announced that it had made a £291m, or 205p-a-share, offer that had been recommended by the Mowlem board.
At the time Carillion said that it would wipe £120m off Mowlem's balance sheet if the deal went ahead.
The situation became more complex when Balfour Beatty said it was also considering the possibility of making an offer for Mowlem.
In response Carillion improved its offer to £313m and Balfour Beatty pulled out of the race two weeks ago after agreeing to buy two of Mowlem's businesses - Edgar Allen and US-based Charter - for about £20m if Carillion's bid was successful.