Sundström studied chemistry at Umeå University, obtaining his PhD in 1977. During his study, he visited Bell Labs and worked under Peter Rentzepis. Upon his return to Sweden, he started building the first ultrafast spectroscopy laboratory in Scandinavia at Umeå University and later at Lund University in Sweden. In 1994, Sundström was appointed professor of Chemical Dynamics and head of the Chemical Physics Department at Lund University. His group's research centers on the photophysics and photochemical processes in model systems of natural and artificial photosynthetic light harvesting, such as bacteriochlorophyll, carotenoids, transition metal complexes, organic and perovskite solar cells.
Sundström was an editor of the journal Chemical Physics Letters.