It follows the decision in November to electrify the sections between London Paddington, Didcot, Newbury and Oxford. It will be Wales’ first main line electrified railway and will cut 17 minutes from Cardiff to London journeys and 22 minutes from Bristol to London journeys.
Massive investment in new trains has also been cleared.
Transport secretary Philip Hammond said: "Alongside our plans for High Speed Rail, it completes a picture of massive upgrades to our intercity rail corridors over the coming years.
"Whilst this is, of course, subject to the government continuing to be satisfied that the proposal offers value for money as the commercial negotiations are concluded and that the final arrangements are compliant with the United Kingdom's EU obligations, I expect that the first of the new trains will be in service by 2016."
He added: "We have also established that a strong high-level case may exist for electrifying some of the Valley lines north of Cardiff. My department will now work with the Welsh Assembly Government to develop a business case for the electrification of the Cardiff Valley lines."
The £4.5bn Intercity Express Programme (IEP) programme will see the building of a combination of around 100 electric trains and bi-mode (diesel and electric) intercity trains which will run to Great Western Main Line stations including Oxford, Swindon, Reading, Cardiff, Swansea, Bath and Bristol and to East Coast Main Line stations such as Peterborough, York, Doncaster, Newcastle, Edinburgh, Aberdeen and Inverness.
The electrification of Great Western Main Line creates the option of extending Crossrail further to Reading, with Reading station also getting a £425m major upgrade which will cut bottlenecks and delays.
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