The planned halls of residence project involves four stepped main buildings rising to 25 storeys.
A deal to buy the Greetham Street site from Portsmouth City Council will now be completed and the search for a contractor started.
Richard Simpson, managing director of property for Unite Students, 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.
“The site is ideal for University of Portsmouth students, being close to campus and will provide a safe and modern home that supports students’ success.”
Unite said the high-rise student block will be built in time for the 2016/17 academic year.