Åström started his academic career as a student of Axel W. Persson at Uppsala University and subsequently became a student of Einar Gjerstad at Lund University where he received his doctoral degree in 1958. His dissertation was called The Middle Cypriote Bronze Age and dealt mostly with the ceramics of that time period. The same year as he received his degree he became the director of the Swedish Institute at Athens where he remained until 1963. After having taught at University of Missouri (1963–1964) and having been the director of the Swedish Institute at Rome (1967–1969) he became professor at University of Gothenburg where he remained for 24 years until his retirement.
Åström formed his own publishing company, Astrom Editions, in 1962. He headed the Swedish part of the Greek-Swedish excavations at Midea in Argolis (1983–1999) and conducted excavations in Dendra together with Nicolaos Verdelis. He held honorary doctorates from University of Vienna (1994), University of Athens (1995) and University of Ioannina (2001) 
- 'Paul Åström in Memoriam', Ann-Louise Schallin, Opuscula 1, 2008, p. 181.
- 'Paul Åström (1929–2008) - the Swedish Nestor of Archaeology', Peter M. Fischer, Opuscula 1, 2008, p. 180.