Beckett now serves on the boards of listed companies Horace Clarkson, BPB, Queens Moat Houses, Learning Technologies and Foreign and Colonial Income Growth Investment Trust. He has been a non-executive director of property company Greycoat and British-Borneo Oil and Gas, and managing director of Consolidated Goldfields.
Chief executive John Armitt said Beckett had a first-class reputation and his appointment was a "significant reason to view the future with confidence".
Costain has also won a £120m contract on section two of the Channel Tunnel Rail Link from Stratford East to Barrington Road in east London in a partnership with Bachy and Skanska.
The contract, awarded by Union Railways (North), will start from Stratford in autumn next year. It calls for two tunnels at a depth of 35 m.
Union Railways has now awarded contracts worth £800m for section two, which extends the new high-speed line into St Pancras Station via east London. Union Railways is set to award contracts worth another £1.4bn this year.
Costain said section one of the rail link, which started in October 1998, was more than 57% complete.