The state-of-the-art teaching and research building at the Headingley Campus will be home to students and academics from the Carnegie School of Sport.
Undergraduate, postgraduate and research programmes will use the Carnegie Teaching and Research building as a base.
And elite athletes will be able to use its outstanding sports science and performance facilities.
It will include an indoor sprint track – cantilevered over the roof – and one of the country’s largest climatic chambers, which can mimic different altitudes and environments.
Professor Peter Slee, vice chancellor of Leeds Beckett University, said: “This world-class facility will underline our global reputation for delivering high-impact sports teaching and research.
“It is part of a wider £200m programme of investment across our campuses, which will further increase the positive contribution we make to our city region and beyond.”
Pete Mackreth, Dean of the Carnegie School of Sport, said: “Many of our academics are international leaders in their field, from anti-doping policy and gender equality in sport to obesity prevention and sports performance.
“This outstanding new facility will help to ensure that our university continues to attract the most talented students and staff to further enhance our reputation for world-leading research in sport.”
It is set to further strengthen the university’s relationships with the city’s top sports clubs.
The new sports development building, which has been designed by architects Sheppard Robson and is being built by Galiford Try, is due to be finished in November 2019.
The Carnegie School of Sport is well-known for its sporting excellence and was founded in 1933 as the prestigious Carnegie College of Physical Training.
Famous sporting alumni from the university include double Olympic gold-winning triathlete, Alistair Brownlee MBE; double Paralympic gold-winning athlete, Kadeena Cox MBE; former GB hockey player Sam Quek, and former England rugby union head coach, Stuart Lancaster.