He studied at the University of Uppsala, where one of his instructors was naturalist Carl Peter Thunberg (1743–1828). In 1800, he accompanied Göran Wahlenberg (1780–1851) on an expedition through Fennoscandia, where he performed entomological and botanical investigations. On the trip he maintained a journal, and in 1917 details of the expedition were published in a book titled I Norrlandsstäder och Lapplandsbygd År 1800. John Erik Forsströms dagbok öfver resan i Norrland och Finnmarken 1800 och i Roslagen 1801.
From 1802 until 1815, Forsström was assigned as pastor on Saint Barthélemy of the Leeward Islands, where he also worked collecting botanical specimens. Afterwards he returned to Sweden, where he died in 1824 at Munktrop, located near the town of Köping.