Reis was born and has always lived in Porto, being one of three children of a chemical engineering professor and a domestic.  Reis spent a small part of his childhood in Metangula, Mozambique, a small town near Lake Niassa, while his father was engaged in military service during the Portuguese Colonial War. He is married with Olga Paiva and has one son, Bernardo Reis (born in 2001). He is a strong supporter of FC Porto.
Reis graduated in Metallurgical Engineering, University of Porto, Portugal, in 1990. He then completed a master's degree at the University of Porto, Portugal, in 1994. Reis did his PhD on Polymer Engineering – Biomaterials, Regenerative Medicine & Tissue Engineering, in the University of Minho, Portugal and Brunel University London, in 1999. He also completed a Doctor of Science (D.Sc.) degree on Biomedical Engineering - Biomaterials & Tissue Engineering, by University of Minho, Portugal, in 2007. 
Reis has also received two Honoris Causa degrees: A first in Medicine from University of Granada, Spain, in 2010 and a second in Engineering from University Polytechnica of Bucharest, Romania, in 2018.