Balfour Beatty said on Wednesday afternoon that it was pulling out of the battle with Carillion to buy Mowlem.
However, in a statement to the stock exchange it said that it had "reached a binding agreement"
Edgar Allen is a UK rail track products manufacturer and Charter is a US-based construction management company. Balfour has agreed to pay a total of about £20m for the two businesses.
The takeover panel had given Balfour Beatty a deadline of today to declare whether it would make a rival bid for Mowlem, after it said it was a possibility on 12 December.