Carillion was selected for the £75m contract in July but has only now formally signed the contract for the job.
Liverpool City Council granted planning permission in September and work on site is now ready to start.
The project will add around 8,500 seats to the main stand, increasing the overall capacity of Anfield Stadium from 45,500 to 54,000.
Completion is scheduled for the third quarter of 2016.
The club also has outline approval for a project to increase capacity of its Anfield Road stand by 4,800.