Wazed Miah was sent to Rangpur Zila School, from where he passed Matriculation in First Division with Distinction in 1956, in 1958 passed Intemediate from Rajshahi Government College, in 1962 he did M.Sc. (Physics) from Dhaka University, First Class First. He has joined the Imperial College, London in 1963 and has done MS in 1964. In 1967 he was awarded the Doctor of Philosophy degree in Physics from Durham University, England. Wazed Miah joined in the Atomic Energy Commission in 1963. He served the Atomic Energy Commission Bangladesh for almost 25 years and eventually retired as its Chairman in 1999.
Dr. Wazed Miah married Sheikh Hasina, present Prime Minister of Bangladesh, elder daughter of the father of the nation Bangabandhu Sheikh Mujibur Rahman on November 17, 1967, when Sheikh Mujib was in jail awaiting the trial of Agartala Case brought against him for "conspiring to secede from Pakistan". They have a son Sajeeb Wazed Joy and a daughter Saima Wazed Putul.