The company acquired the Chaucer House site on Isambard Brunel Road from the city council.
Plans include creating a £30 million student halls facility to provide a home for around 480 students by 2018.
Richard Simpson, MD of Property for Unite Students, said: "The acquisition demonstrates our ability to continue to secure high quality sites in line with our target returns.
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"Students continue to be important contributors to the local economy and this new development will help to meet the high demand for student accommodation in the city.
City Council Leader Donna Jones added: "Providing high quality managed student accommodation in the city is key to assisting Portsmouth's housing shortage.
"The more student accommodation we have in the city, the more private family homes will come into the rental market easing overcrowding in the city."
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