Jakob Hallgrímsson graduated with a diploma in violin performance from the Reykjavík College of Music in 1964. He went to Mosow for further education from 1964-66. In 1976-77 he studied music theory with Dr. Hallgrímur Helgason and at the Musikhögskolan in Stockholm from 1977-78. Jakob studied the organ with Haukur Guðlaugsson and graduated from the Music School of the National Church in 1990. He has also taken various courses in organ performance e.g. with Prof. Gerald Dickel in Hamburg in 1995.
Jakob was a violinist with the Iceland Symphony Orchestra 1960-72. Throughout his career he has taught at various music schools. He has taught at the Music School of Seltjarnarnes from 1982 and at the Music School of the National Church from 1990.