Born on 4 October 1942 into a Bengali Kayastha family at Calcutta in the Bengal state of British India to Kiran Lal Roy-Sujata Sikdar couple, Probir Roy graduated in physics with honours from Presidency College under Calcutta University in 1962 before moving to Cambridge University to obtain an MA (Cantab) from King's College, Cambridge in 1965. Subsequently, he joined Stanford University for his doctoral studies and secured a PhD, mentored by S. M. Berman, for his thesis in Kaon physics, in 1968. During this period, Roy worked at Stanford Linear Accelerator Center as a research assistant (1966–68) and as a temporary research associate (1968). He remained in the US for three more years for his post-doctoral work at Cornell University where he worked at the laboratories of Kenneth G. Wilson, who would go on to receive the Nobel Prize for physics in 1982, and Toichiro Kinoshita, an APS fellow, simultaneously serving the University as an instructor. Before returning to India in 1972, he had a one-year spell at CERN during 1971–72 as a visiting scientist.