Miller, which operates only in the UK, made a £4m loss last year but has exited several loss-making contracts and hopes to return to profit this year.
Galliford and Miller Group have agreed the transfer of Miller Construction with a nil net assets balance, including a cash balance of £23 million.
Greg Fitzgerald, chief executive of Galliford Try, said:
We are delighted to announce the acquisition of Miller Construction, achieved at a very good price and with no net cash consideration. The acquisition brings together two construction businesses with a strong strategic fit and accelerates our strategy of growth into an improving marketplace.