Prof. Gombe was born in Seme, Kisumu District in 1938. He was educated at Maseno School, Makerere College, (1958-1960), London University (1961-1967) and Cornell University (1969-1972). His research interests have been on aspects such as malnutrition, mineral deficiencies, adverse environmental and parasitic infections that may cause infertility. He demonstrated that many of these factors (including tryponasomiasis) impair reproduction by damaging certain areas of the brain. He has examined male fertility and how it can be controlled for family planning purposes. Long-term safety of contraceptive drugs is his special concern.
Prof. Gombe has lectured at the Department of Animal Physiology, University of Nairobi since 1968. He has published over 60 scientific papers, mainly in the area of reproductive physiology and endocrinology. He is a member of 12 national and international scientific organizations. He is a Fellow of the Third World Academy of Sciences. He is the Secretary and Founder Fellow of African Academy of Sciences. He is currently the Director of Reproductive Biology Unit, a constituent of the National Centre for Research in Reproduction which he helped to found.