After a PhD^[13] in computer science and engineering from the Tokyo Institute of Technology, during which he also worked as a research scientist at the Kawato Dynamic Brain Project in ATR, Kyoto, Vijayakumar became a postdoctoral fellow in the Laboratory for Information Synthesis, RIKEN Brain Science Institute, Saitama, Japan working with Professor Shun'ichi Amari. He then headed to the University of Southern California^[14] as a presidential postdoctoral fellow with Professor Stefan Schaal and subsequently became a research assistant professor (2001–2003) in the Department of Computer Science at USC, Los Angeles.

In 2003, he moved to the University of Edinburgh, where he went on to become director of the Institute for Perception, Action and Behaviour in the School of Informatics and then Co-Director^[15] of Edinburgh Centre for Robotics.

In 2007 Vijayakumar was awarded a Royal Academy of Engineering Senior Research Fellowship in Learning Robotics, co-funded by Microsoft Research.^[16] He is a Turing Fellow since 2018 and a Fellow of the European Laboratory on Learning and Intelligent Systems (ELLIS) since its inception in 2020.

Vijayakumar is an active science communicator, giving public talks and media interviews. In 2015 the University of Edinburgh awarded him its annual Tam Dalyell Prize for Excellence in Engaging the Public with Science^[17] and in 2016 he presented a series of robot demonstrations at the television launch^[18] of BBC micro:bit live lessons. He featured in Stargazing Live with Dara O Briain, March 2017. He was a judge on the 2016-2018 revival of the robot combat TV show Robot Wars. Vijayakumar also delivered two TEDx talks on robotics and machine learning at TEDx Glasgow^[19] 2018 and TEDx Edinburgh^[20] 2015.