Giuseppe Koch was born in Rome on November 11, 1937, a descendent of a Tyrolean family whose ancestor, the painter Josef Anton Koch, emigrated to Rome in 1795. After graduating from the Mamiani High School in Rome (1955) in classics, where he was active in scouting, and three years of studies in engineering, he entered the Society of Jesus in 1958. During his Jesuit formation he obtained a degree in philosophy at the Gregorian University in Rome; and in 1970 a degree in theology at Leuven-Eeghenoven (in Belgium). He was ordained a priest in 1969.
In 1966 he obtained his degree in mathematics and physics from the University of Rome (La Sapienza) with a thesis in experimental physics in the field low temperature physics, carried out at the CNEN (National Committee of Nuclear Energy) in Frascate (which later became ENEA, the National Institute for Alternative Energy). From 1970 to 1988 he taught physics and theology at the Jesuit schools in Rome and Palerma while also active in youth chaplaincy. For many years he served as Dean of Science at the Massimo Institute in Rome, and in pastoral work at universities in Rome and Florence.
From 2001 to 2009 he was superior of the Jesuit community at the Vatican Observatory and vice director for administration. He then returned to pastoral work in university chaplaincy and at the Massimo until 2015, when he returned to the Vatican Observatory as librarian while continuing his pastoral activities. While at the Observatory he has written various popular articles about extrasolar planets and gravitational waves.