Robert Geoffrey Edwards was born in 1925 in Manchester.

He studied Biology at the University of Wales between 1948 and 1951, and the University of Wales between 1951 and 1957. He received his doctorate in 1955 with a thesis on embryonic development in mice. He spent one year at the California Institute of Technology. He later joined the team of the National Institute of Medical Research in Mill Hill, England, in 1958.

In 1962 he moved to the University of Glasgow and later to the University of Cambridge. In 1965 he was visiting professor at John Hopkins University and in 1966 at the University of North Carolina. He returned to England in 1969 as a 'reader' of the Ford Foundation in Physiology, where he remained until 1985.
In 1967 he began his collaboration with Patrick Steptoe, with whom he founded the first IVF Clinic in Bourn Hall in Cambridge. In 1984 he also worked at the Free University of Brussels.

In 1985 he was appointed Professor of Human Reproduction at the University of Cambridge, where he retired in 1989 and received the title of Emeritus.

He was president of the European Society of Human Reproduction and Embryology between 1984 and 1986. He has received awards and recognitions from various institutions around the world.
One of his most known works is Principles of Assisted Human Reproduction, with Steven A. Brody.

In 2010 he was awarded the Nobel Prize in Medicine and Physiology for the development of in vitro fertilization.