The last gasp offer comes ahead of this Thursday, which is the deadline under takeover rules, after which Carillion would have to wait six months for any further approach.
As expected, it is a sweetened deal, which offers Balfour shareholders 58.268% of the combined company - up from the previous 56.5%.
Shareholders would also get a cash dividend of 8.5 pence per share.
The new terms value Balfour at £2.1bn (US$3.5 billion).
The pair and the merger plan haven't been out of the news much recently since they revealed in June they were first in talks over the creation of a potential £3bn mega construction firm.
Philip Green, Carillion chairman said today: "Given the scale of the prize for shareholders of both Balfour Beatty and Carillion from a merger of the two companies, the board of Carillion remains committed to moving forward in a constructive and collaborative way with the board and management of Balfour Beatty to create a world-class business and very significant value for the shareholders of both companies"
Balfour shares added 3.87% on Tuesday.