Mouchel, which includes landscape architecture and urban design among its services, began negotiations with Costain in December. The firm also rejected an offer from construction and support services firm Interserve.
Mouchel's announcement comes as the firm reported a 73 per cent drop in pre-tax profits in the six months to 31 January and 13 per cent fall in revenue to £270.3m.
Chief executive Richard Cuthbert said it had been a challenging period but the outlook was positive. "We remain confident in Mouchel as an independent business."