Fleming received a B.S. (with honors) degree in Chemistry from the University of Bristol (1971) and a Ph.D. degree in Physical Chemistry from the University College London (1974). He spent the next five years as a postdoctoral researcher at three institutions: California Institute of Technology (1974–1975); University of Melbourne (1975–1976); and the Royal Institution in the United Kingdom (1976–1979).
In 1979 Fleming received his first academic appointment, as assistant professor at University of Chicago (1979–1983). In 1983 he was appointed associate professor, and in 1985 he was made a full professor (A. H. Compton Distinguished Services Professor). He filled that position until 1997, when he accepted a dual position at the University of California, Berkeley as professor in Chemistry and as the first director of the Physical Bioscience Division of the Lawrence Berkeley National Laboratory; in 2002 he was given the chair of Melvin Calvin Distinguished Professor of Chemistry at UCB. In April, 2009, Fleming was appointed UCB's vice chancellor for research, responsible for administering all federal, state and private research funds received by the campus and overseeing all campus museums and research units. He resigned under protest  from this position following accusations of sexual harassment by a previously fired UCB employee. Many UCB faculty members questioned the fairness of UCB's investigation, which provided no mechanism for appeal.
Fields of study pursued by Fleming and his study groups include condensed-phase chemical and biological dynamics, photosynthesis operations, quantum dynamics, quantum information in condensed phases, photochemical reactions, electronic processes at nanoscale, and development of nonlinear optical spectroscopes.
He was the first to apply two-dimensional electronic spectroscopy to photosynthetic systems. He got particularly known for the work published in 2007 claiming evidence for quantum coherence in photosynthetic energy transfer, an explanation of the high efficiency of photosynthesis. This interpretation of the observed spectra has since been proven incorrect.    
- Carotenoid Cation Formation and the Regulation of Photosynthetic Light Harvesting. (co-author), Science 307, 433-436 (2005)
- Two-dimensional Spectroscopy of Electronic Couplings in Photosynthesis. (co-author), Nature 434, 625-628 (2005)
- Evidence for wavelike energy transfer: Quantum coherence in photosynthetic systems. (co-author), Nature 446, 782 (2007)
- Coherence dynamics in photosynthesis: Protein protection of excitonic coherence. (co-author), Science 316, 1462 (2007)
- Architecture of a Charge-Transfer State Regulating Light Harvesting in a Plant Antenna Protein. (co-author), Science 320, 794-796 (2008)
- made a Fellow of the American Academy of Arts and Sciences (1991)
- made a Fellow of the Royal Society of London (1994)
- received an award from the Inter-American Photochemical Society (1996)
- received an award from the Royal Society of Chemistry (1996)
- presented the Centenary Lecture to Royal Society of Chemistry (1996)
- presented the Max T. Rogers Distinguished Lectureship lecture at Michigan State University (1997)
- received the Peter Debye Award in Physical Chemistry from the American Chemical Society (1998)
- received the Harrison Howe Award in Physical Chemistry from the ACS (1999)
- received the Earle K. Plyler Prize for Molecular Spectroscopy from the American Physical Society (2002)
- received the Sierra Nevada Distinguished Chemist Award (2003)
- received the Porter Medal from the European Photochemistry Association (2004)
- made a Member of the United States National Academy of Science (2007)
- presented the Presidential Lecture to Iowa State University (2008)
- received the Ahmed Zewail Award in Ultrafast Science and Technology from the ACS (2008)
- received the Joel Henry Hildebrand Award in the Theoretical & Experimental Chemistry of Liquids from the ACS (2009)
- UC Berkeley website
- UC Berkeley press release
- The Daily Californian, April 13, 2015
- The Daily Californian, May 4, 2012
- The Daily Californian, April 20, 2015
- Chemical & Engineering News, 93(16), April 17, 2015
- G. S. Engel; T. R. Calhoun; E. L. Read; T. K. Ahn; T. Mancal; Y. C. Cheng; R. E. Blankenship; G. R. Fleming (2007). "Evidence for wavelike energy transfer through quantum coherence in photosynthetic system". Nature. 446: 782–6. doi:10.1038/nature05678. PMID 17429397.
- Quantum secrets of photosynthesis revealed, April 12, 2007, physorg.com (retrieved June 4, 2011)
- R. Tempelaar; T. L. C. Jansen; J. Knoester (2014). "Vibrational Beatings Conceal Evidence of Electronic Coherence in the FMO Light-Harvesting Complex". J. Phys. Chem. B. 118: 12865–12872. doi:10.1021/jp510074q.
- N. Christenson; H. F. Kauffmann; T. Pullerits; T. Mancal (2012). "Origin of Long-Lived Coherences in Light-Harvesting Complexes". J. Phys. Chem. B. 116: 7449–7454.
- E. Thyrhaug; K. Zidek; J. Dostal; D. Bina; D. Zigmantas (2016). "Exciton Structure and Energy Transfer in the Fenna−Matthews− Olson Complex". J. Phys. Chem. Lett. 7: 1653–1660. doi:10.1021/acs.jpclett.6b00534.
- A. G. Dijkstra; Y. Tanimura (2012). "The role of the environment time scale in light-harvesting efficiency and coherent oscillations". New J. Phys. 14: 073027. doi:10.1088/1367-2630/14/7/073027.
- D. M. Monahan; L. Whaley-Mayda; A. Ishizaki; G. R. Fleming (2015). "Influence of weak vibrational-electronic couplings on 2D electronic spectra and inter-site coherence in weakly coupled photosynthetic complexes". J. Chem. Phys. 143: 065101. doi:10.1063/1.4928068.
- Halpin, A.; Johnson, P.J.M.; Tempelaar, R.; Murphy, R.S.; Knoester, J.; Jansen, T.L.C.; Miller, R.J.D. (2014). "Two-Dimensional Spectroscopy of a Molecular Dimer Unveils the Effects of Vibronic Coupling on Exciton Coherences". Nature Chemistry. 6: 196–201. doi:10.1038/nchem.1834.
- UC Berkeley website
- The Fleming Group at UC Berkeley webpage
- Chemical & Engineering News, 23 February 2009, "2009 ACS National Award Winners", pp. 64-65