Thompson obtained a B.A. from Duquesne University, Pittsburgh, Pennsylvania, USA, in 1962, and his PhD at Temple University, Philadelphia, Pennsylvania in 1976.

Thompson has held positions at the University of Dayton (Instructor in theology, 1964—65), University of Detroit (Assistant Professor: Old Testament, 1967—69), Tübingen Atlas of the Near East (research associate, 1969—76), École Biblique (visiting professor, 1985—86), Lawrence University (visiting associate professor, 1988—89), and Marquette University (associate professor, 1989—93), and was professor of theology at the University of Copenhagen from 1993-2009. He was named a National Endowment for the Humanities Fellow in 1988. He is general editor for the Equinox Press monograph series Copenhagen International Seminar and associate editor of the Scandinavian Journal for the Old Testament, and serves on the editorial boards of the journals Holy Land Studies and Dansk Teologisk Tidsskrift.

The focus of Thompson's writing has been the interface between the Bible (specifically the Old Testament) and archaeology. His The Historicity of the Patriarchal Narratives (1974), was a critique of the then-dominant view that biblical archaeology had demonstrated the historicity of figures such as Abraham and other Biblical patriarchs. His The Early History of the Israelite People From the Written and Archaeological Sources (1993) set out his argument that the biblical history was not reliable, and concludes: "The linguistic and literary reality of the biblical tradition is folkloristic in essence. The concept of a benei Israel ... is a reflection of no sociopolitical entity of the historical state of Israel of the Assyrian period...." In How Writers Create a Past (US title: The Mythic Past: Biblical Archaeology and the Myth of Israel), he argued that the bible was entirely, or almost entirely, a product of the period between the 5th and 2nd centuries BC. The Bible in History is widely used as a set-text in undergraduate courses in biblical studies.

Thompson is closely associated with the movement dubbed biblical minimalism by detractors (other major figures include Niels Peter Lemche, Keith Whitelam, and Philip Davies), a loosely-knit group of scholars who hold that the bible's version of history is not supported by any archaeological evidence so far unearthed, indeed undermined by it, and that it therefore cannot be trusted as history.

His formative study, The Historicity of the Patriarchal Narratives, (Albright's reputation "never recovered from Thompson's critique"), but the controversy it provoked with conservative American academia prevented him from obtaining a tenured position in any North American university. His later works have been received in a similar fashion in North America, but have been widely accepted in Europe.

In 1992 he published The Early History of the Israelite People, and in 1993 joined the Faculty of Theology at the University of Copenhagen as a full professor. The remainder of the decade of the 1990s was dominated by sometimes harsh fighting between conservative North American scholars (often termed "maximalists"), exemplified in a 2001 exchange between Iain Provan, Thompson and Philip R. Davies of the University of Sheffield in the "Journal of Biblical Studies"..

Some maximalist authors have written that recent archaeological discoveries appear to undermine Thompson's theories. One such discovery is the Tel Dan Stele. Thompson's interpretation of this stele (uncovered during or before the mid 1990s) and other such discoveries are written up in his book The Mythic Past (1999) and other works.