The contractor is understood to have beaten off rivals BAM, Sir Robert McAlpine and Mace to take the prized university job.
The 23,000 sq m student centre at Gipsy Lane will consist of a lecture theatre, library and teaching accommodation.
The original plans were knocked back by Oxford’s planning committee last year but were successfully revised to gain consent in the spring.
The new building will boast a 20% reduction in carbon emissions for the existing site, which will see some buildings demolished during the two-year build.
The roof will be fitted with 600 sq m of solar panels and 3, 000 sq m of ‘green’ sedum roof.