The firm will start work this summer on Phase 3C, the final two Frank Gehry-designed buildings that will complete Electric Boulevard.
Balfour Beatty and Morgan Sindall ranked second and third respectively helped by infrastructure new orders.
Balfour picked up a £125m deal for maintenance of the Leeds inner ring road and a £62m deal for flood protection work in Suffolk while Morgan Sindall was confirmed as main delivery partner for the Portishead railway project.
Top 10 ranking for work won in June
Click for full interactive tables of contractor and client rankings
Across the wider market, the top 50 contractors saw new orders in June hold level at around £3.1bn.
In the rolling 12-month rankings of work won, Strabag held top spot, buoyed by its £3bn long-term Haweswater Aqueduct Resilience Programme contract, with Mace ranking second and Balfour Beatty placed third, according to data compiled by Barbour ABI.
Top 5 ranking for work won in last 12 months
Click for full interactive tables of contractor and client rankings
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