The £80m development is expected to accommodate more than 1,000 students when it opens in 2020.
Subject to planning, Unite Students is paying London & Scottish Property £10.5m for the 21,000 sq ft site, which currently provides leisure accommodation over two levels, next door to the 19-storey Arena Point office tower, which is not part of the sale deal.
Group property director Richard Simpson said: “Leeds is a strong performing market with two high quality Universities. Unite has maintained a 99% occupancy rate in the city over the past five years, signalling we have room to expand and there is demand for the quality, affordable student accommodation we provide. We are confident the site in Leeds – subject to planning approvals – will be a great addition for Leeds' growing number of students."