The 22 tube assemblies will require 150 workers at Rosyth in Fife and Bristol.
The contract is part of the common missile compartment (CMC) project for the UK Successor and US Ohio Class replacement submarine programmes.
The work will get under way towards the end of this year.
It is expected to complete in the early 2020s.
The contract was awarded to Babcock by US defence contractor General Dynamics Electric Boat.
Successor-class submarines are due to replace the current Vanguard fleet, which carry Trident missiles.
The contract announcement was made by the UK government as the SNP conference re-affirmed its opposition to nuclear weapons.
UK Defence Minister Harriett Baldwin said: "I am delighted that Babcock have secured this critically-important project.
"This contract is a strong endorsement of our highly-skilled and globally-competitive defence industry and will secure hundreds of jobs in Rosyth.
"With Faslane set to be home of all the Royal Navy's submarines by 2020, this is further evidence of the benefits that defence brings to the economy and to Scotland."
Defence contractor Babcock International has secured an £80m order to make part of the missile launch silos for the next generation of Royal Navy nuclear-armed submarines.