Morgan Sindall had initially been in negotiations to take the building forward as preferred contractor but Kier is now understood to be in place to start the job.
The proposed building will provide over 100,000 sq ft of academic space, which will be accessible to all Bournemouth University students and the local community.
It will be between five and seven storeys high, and occupy a prominent site overlooking the Wessex Way.
The development will primarily be used by more than 4,000 students from the Faculty of Health and Social Sciences, which is currently based in numerous buildings on Christchurch Road.
The faculty trains nurses, midwives and paramedics as well as other health professionals and researchers. It also houses the National Centre for Post Qualifying Social Work.
The project is targeting a BREEAM Excellent rating.
As part of the Lansdowne project, Three Sixty Developments is also developing student accommodation with up to 550 beds.
