Engeström was enrolled in 1756 as an auskultant – an unpaid civil servant allowed to take part in the agency's negotiations – at the Swedish Board of Mines.
He studied chemistry and mineralogy under Anton von Swab [sv], Henrik Teofilus Scheffer, Georg Brandt and Axel Fredrik Cronstedt, learning from the latter the practicalities of mining, and undertook study trips to Norway (1760) and England, the Dutch Republic, and Prussia (1764).
In England, he trained in chemistry, including in William Lewis' laboratory, and continued the translation of Cronstedt's mineralogy book into English.
He became known for his description of the use of the blowpipe (which came from Cronstedt) in the analysis of minerals, originating from lectures during his stay in London in 1765 and which was subsequently translated into Swedish as Nyttan af blåsröret i mineralogien.
In its journal Vetenskapsakademiens Handlingar [sv] there are ten minor essays by him, all in chemistry and mineralogy, and he left a couple of speeches.
From his uncle Mathias Benzelstierna [sv], von Engeström inherited the Vrå estate in Tibble Parish.
Johan [sv] (1743–1807) was a politician (a member of the aristocratic opposition against the king and also suspected of participating in the conspiracy against Gustav III.