The four-year package understood to be worth £350m will include the construction of three marine tunnels to form part of the vital cooling system for the nuclear power station.
The project involves driving a total of 9.5km of both onshore and offshore tunnels of around 7m diameter.
Balfour Beatty was originally bidding for the scheme in joint venture with Morgan Sindall. But EDF Energy opted for Costain in the original rounds of bidding in autumn 2013.
The decision to switch contractor is a blow to Costain, which had mobilised and started design work on the water cooling systems.
It is the second major package Balfour Beatty will deliver at Hinkley Point C, following its appointment to the £460m electrical works package in joint venture with NG Bailey in 2015, which is currently on site.
Stephen Tarr, managing director Balfour Beatty’s Major Projects business, said: “Hinkley Point C is a project which inspires collaboration by its very nature due to its significant scale and complexity.
“Our expert engineers will deploy heavy civil engineering skills and extensive knowledge of tunnelling.”
Costain refused to comment about the decision.