Property investment firm Ace Liberty and Stone sold Hume House in Leeds to Olympian Homes after buying it for £1.7m in March 2014.
Construction work started on the new 37-storey building this week.
Once complete, it will include 752 bedrooms of purpose-built student accommodation, along with a roof terrace on the 35th floor. At its peak, it will create over 300 construction jobs.
The 278,000 sq ft scheme on Tower House Street will be the tallest building in Yorkshire and the North East with a height of 114.3m.