Midas will build five additional blocks of accommodation with 224 rooms for the Glasney Student Village at the Tremough Campus.
Preparatory work has now started, with the accommodation due to be ready for the 2012 academic year.
Midas has also recently been awarded a £7m contract to build new education facilities catering for art, design, construction and automotive engineering students at Truro College.
Mike O’Neil, Midas Construction executive director in Devon and Cornwall, said: “We have built all the existing student residences on the Tremough site and this summer handed over phase II of the £29m development of Penwith College in Penzance.
Niamh Lamond, CEO of the Tremough Campus Services Group, said: “This latest phase of development forms part of the institutions’ strategy to ensure that there is sufficient high quality accommodation for students in the locality, in line with the growth of UCF and UoE.
University of Exeter Deputy Vice-Chancellor, Professor Mark Overton, said: “The University of Exeter is in the midst of an investment programme worth more than £350m across its three campuses in Devon and Cornwall.
“Through this investment, we will provide world-class facilities for our students. This new project will help ensure we continue to provide excellent campus accommodation for our students.”