Gaffin was born to missionaries in China. He received a B.A. from Calvin College (1958), a B.D. (1961), Th.M. (1962), and Th.D. (1969) from Westminster Theological Seminary, and undertook graduate studies at Georg-August University of Göttingen (1962-1963). He has taught at Westminster since 1965. He is an ordained minister in the Orthodox Presbyterian Church.