Professor Burrage completed his PhD in Computational Mathematics from the University of Auckland in 1978. In his early academic years he was at the University of Auckland (NZ), the University of Sussex (UK), the University of Liverpool (UK).

In 1991 he was appointed to the Chair of Computational Mathematics the University of Queensland.  He established the Advanced Computational Modelling Centre at the University of Queensland in 1995 and was Director of that  centre for 12 years.  He was also the founding CEO of the Queensland Parallel Supercomputing Facility in 1999.

He was awarded a Federation Fellowship of the Australian Research Council from 2003-2008. In 2008 he was made Professor of Computational Systems Biology in the Computational Biology group  within both the Department of Computer Science and  the Centre for Integrative Systems Biology  at the University of Oxford. He had this position until October 2015. He shared his time between Oxford and as Professor of Computational Mathematics at QUT, from  2010 until 2015 and  continues in this role at QUT.

He was made a Visiting Professor to the Department of Computer Science at the University of Oxford from 2016 to 2019. His current research interests are in Computational Mathematics and Computational Biology.