He was born on January 24, 1951 in Tbilisi. Studied at Tbilisi #4 Public School. In 1974 he graduated from Tbilisi State Medical Institute.
In 1978 he was appointed as a laboratory assistant to the Head of the Department of Allergology at the same institute.
From 1991 to 1996 he was the Head of the Department of Allergic Disease Epidemiology and Research Immunogenetics at the Institute of Research and Experimental Medicine of the Medical University.
1988-1996 - Head of the Department of Allergic Diseases Epidemiology and Immunogenetics, Tbilisi State Medical University, Institute of Clinical and Experimental Medicine;
1995-1997 - he worked as the director of the National Center for Health Management.
1997-2001 - he was the First Deputy Minister of Health of Georgia; 2001-2004 - Minister.
Since February 7, 2013, Gamkrelidze has been the Director General of the National Center for Disease Control and Public Health.
Gamkrelidze has publications on healthcare organization, medical education, current scientific issues and healthcare development in Georgia.
In 2002, the Association of Diabetic Children awarded Amiran Gamkrelidze with the Gold Medal of the Association for Outstanding Care and Assistance to Diabetic Children Living in Georgia. In connection with Tbilisoba, on October 3, 2020, along with eight doctors fighting the COVID-19 pandemic, he was awarded the title of Honorary Citizen of Tbilisi.
He has a wife and two children.