The 665-home development is being constructed on behalf of Highline Investments at the Monk Bridge site to the south west of Leeds city centre.
Galliford Try beat Sir Robert McAlpine to take the project which is expected to get underway in the Autumn.
There will be a mix of one, two and three-bedroom apartments across five different blocks, which will vary from 12 to 22 storeys in height.
In addition, the adjacent railway arches will be refurbished to accommodate retail and hospitality units.
Bill Hocking, chief executive of Galliford Try, said: “We are delighted to be able to start work on such a prestigious development in the heart of Leeds.
“This scheme is a significant investment in the current economic environment and our excellent track record in the private rental sector has led Highline to place their trust in Galliford Try to deliver for their customers.”
The Leeds office of Buro Happold is the mechanical and electrical consultant, with Roscoe acting as structural engineer and Gardiner & Theobald cost consultant.