Work will see the creation of a new home for the Carnegie School of Sport.
It will include research laboratories, an indoor rooftop sprint track for performance training and analysis and a roof walking track and terrace.
Cliff Wheatley, Managing Director for Galliford Try North East and Yorkshire, said: “We are delighted to be working with Leeds Beckett on such a prestigious project.
“We have a proven track record in providing high-quality buildings for higher education and we look forward to working with the University to ensure that their students and staff have the world-class sports science facilities they demand.”
Professor Peter Slee, Vice-chancellor of Leeds Beckett University, said: “This £45m 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.”
Construction is due for completion in Autumn 2019.