Planning approval from Carmarthenshire Council will allow Carillion engineers to start the £16m contract to build a viaduct capable of carrying two tracks.
Originally engineered by legendary Isambard Kingdom Brunel, the viaduct was constructed in 1852, although its superstructure was replaced early in the twentieth century.
The job forms part of a Network Rail and Welsh Government jointly funded £40m plan to improve rail infrastructure along the route, which will also see 6 miles of new track built between Cockett West Junction and Duffryn West Junction.
Passengers levels using railways in West Wales are forecast to rise by 20% by 2020.
The plans will meet that demand, allowing two extra trains per hour between Swansea and Llanelli and one extra an hour between Swansea and Carmarthen.