Teschendorff completed a B.Sc. (Honors) in Mathematical physics from the University of Edinburgh in 1995. In 1996, he obtained a distinction in the Certificate of Advanced Study in Mathematics from the University of Cambridge. Later, in 2000, he earned a Ph.D. in Theoretical particle physics from the University of Cambridge. He performed post-doctoral work at the Breast Cancer Functional Genomics Laboratory at the University of Cambridge from 2003 to 2008. Teschendorff was a member of the Research Group at British Telecom Labs from 2000 to 2001 before joining the University of Warwick as a research assistant within the Mathematical Biology Group, where he remained from 2001 to 2003. He was a senior post-doctoral fellow in Computational Biology at the University of Cambridge between 2003 and 2008. In 2008, he joined University College London where he held the positions of principal research associate in Statistical Cancer Genomics until 2013, as well as Newton Advanced Fellow from 2015 to 2018. He then joined the CAS Max-Planck Partner Institute of Computational Biology in Shanghai, where he was a professor in Computational Systems Epigenomics from 2013 to 2020. Since 2020, he has been a professor and principal investigator at CAS Key Lab of Computational Biology in Shanghai, and in 2015, was named an honorary research fellow at University College London. He has been a recipient of the Heller Research Fellowship, Cambridge-MIT fellowship, and an Advanced International Newton Fellowship from the Royal Society. In 2023, he was a recipient of a Highly Cited Researcher award from Clarivate.