As an undergraduate, Gibson was awarded the R.D. Haworth medal for finishing top of his graduating year at the University of Sheffield and, following completion of his D.Phil at Oxford, was awarded a NATO fellowship to carry out postdoctoral research at the California Institute of Technology. While a lecturer at the University of Durham he was awarded the BP Young University Lecturer award, rapidly followed by the Sir Edward Frankland Fellowship of the Royal Society of Chemistry. Following his move to Imperial College, he received the Corday-Morgan medal and prize of the Royal Society of Chemistry, primarily for work he had completed at Durham on fundamental organometallic chemistry. An industrially sponsored Royal Society of Chemistry Award for Organometallic Chemistry followed in 1999.  He received the prestigious Joseph Chatt Lecturer award of the Royal Society of Chemistry in 2001 followed by the Tilden Lectureship of the Royal Society of Chemistry in 2004. He was elected to the Royal Society in 2004.