The scheme, known as Fabrik, is a 216-home development for the private rented sector.
The developer is Leeds-based Oakapple Group but Grainger is forward funding the scheme and will add it to its portfolio of PRS investments in Leeds on completion, which is anticipated for late 2021.
Oakapple gained planning permission for the 12-storey block in May 2019 and has now finalised its funding deal with Grainger. Tolent is the main contractor.
Grainger chief executive Helen Gordon said: "We are pleased to announce start on site of our latest investment in Leeds, one of our target regional cities, which will deliver 216 new high quality, purpose built rental homes. Fabrik will complement our 242-home Yorkshire Post development, also in Leeds, thereby providing over 500 PRS units in Leeds once these schemes are delivered."
Oakapple Group chairman Philip Taylor added: "Oakapple are delighted to be working with Grainger on delivery of this project. As a Leeds business we are particularly pleased to see a major institution committing further to our city. It is a vote of confidence in the South Bank and hopefully a catalyst for further schemes to come forward in the area".