The site will provide accommodation for 836 students and completion is anticipated for September 2016.
The 0.8-acre Greetham Street site is being acquired from Portsmouth City Council.
Unite Students already has three properties in the city that house 1,400 students studying at the University of Portsmouth.
Unite Students managing director of property Richard Simpson said: "The acquisition forms part of our regional development strategy where there is a growing demand for student accommodation. This year we have seen university applications continue to outstrip available places and there is a growing need for safe, secure purpose built student accommodation.”