The early contractor involvement contract will see Atkins deliver engineering design and TACP environmental support on the bypass, which comes with an estimated price tag of £55m.
The team will develop the design of the preferred A483-A489 route alignment, taking it through the statutory process before carrying out construction.
Transport Minister Edwina Hart said: “It is also encouraging to see that a Welsh company has won this tender, which will help safeguard Welsh jobs and result in money staying in the local economy,” she said.
The procurement process was conducted under the OJEU Restricted Procedure. Following a pre-qualification competition, five contractors including Balfour Beatty and Carillion were invited to tender for the contract.
Construction is scheduled to start at the end of 2014.