Gregory received his MSc in Mathematics in 1979 from Gomel State University, Belarus. He worked in high school and research institutes of Belarus from 1979-1990. He studied for PhD under Professor Noga Alon at the School of Mathematics, Tel Aviv University, Israel and received his PhD (with distinction) in 1993. Between 1993 and 1996 he held visiting positions in the Department of Mathematics and Computer Science, Odense University, Denmark and then became a lecturer at the Department of Mathematics, Brunel University, UK. In 1996 he was awarded Kirkman Medal of International Institute of Combinatorics and Applications.

Since 1st September 2000, Gregory has been Professor of Computer Science, Department of Computer Science, Royal Holloway, University of London. He held Royal Society Wolfson Research Merit award in 2014-2018 and was elected to Academia Europaea in 2017 and to AAIA (Asia-Pacific Artificial Intelligence Association) in 2021. He received best paper awards at information security access control symposium ACM SACMAT in 2015, 2016, 2021 and 2022. In 2019 he was presented with Amity Global Academic Excellence Award and in 2022 with AAIA Outstanding Contribution Award.

Gutin's main research interests include graphs and combinatorics, parameterized, polynomial, exact and approximation algorithms,  access control in information security, combinatorial optimization and theoretical economics. G. Gutin published two editions of a monograph (translated into Chinese) and edited two books. He has more than 250 papers published or accepted for publication in refereed journals and conference proceedings, and 16 chapters and sections in edited books. His publications were cited over 11900 times.