Amey was awarded the renewal contracts for the Great Western region, which comprises the West Country and Wales.
Balfour will work in the Southern region and in East and West Anglia, including north-east London. The contract is estimated to be worth £113m in the first year.
Carillion will renew track in the West Midlands and upgrade switches and crossings in the West Midlands, North-west and Great Western region in a deal worth about £50m in its first year.
Its existing £15m contract on the West Coast Main Line will continue.
Amey this week appointed as its chairman Sir Patrick Brown, the former permanent secretary at the Department for Transport.