Born Jonas Toresson (later changed to Alström) in the town of Alingsås in Västergötland, in 1707 he became a clerk for Stockholm merchant Alberg in London. Alberg's business failed after about three years, but Alström became a shipbroker on his own, and did very well.
Eventually he desired to establish industry back home, and in 1724 established a woolen factory in his native village, which became profitable after some initial difficulties. He then established a sugar refinery in Gothenburg, encouraged improvements in potato cultivation, tanning, cutlery, and shipbuilding. His greatest success came with the introduction of sheep.
He was one of the six persons who founded the Royal Swedish Academy of Sciences in 1739.
The court honored him with a knighthood of the Order of the North Star in 1748, and soon after with letters of nobility, changing his name to Alströmer.
Jonas Alströmer had four sons in two marriages, Patrik Alströmer, August Alströmer (father of Anna Margaretha Alströmer), Clas Alströmer and Johan Alströmer. His son Clas Alströmer was a noted naturalist.