Eino Forsström attended the Finnish Reali Lyceum in Helsinki. He competed twice at the Olympic Games, winning two medals: bronze at 1908 London in the gymnastics team event and silver at 1912 Stockholm in the free system team event. In addition to gymnastics, Forsström was an active boxer trained by well-known coaches.
Forsström joined the Lars Krogius shipping company in Helsinki and from 1914 managed the Rauma branch and later the Pori branch of the company. In the 1920, he became assistant manager of G. E. Ramberg Oy, a trading company based in Pori. Since 1925, he was sales manager of the Rettig tobacco factory, which had its roots in Hamburg in Germany. Eventually, he was appointed managing director of the Malta Oy in Helsinki, a food and tobacco company, in 1937. He married Irene Matilda “Lilli” Larsson and had two daughters and one son with her.