He switched to sprinting as a 15-year-old after his athletics club, Turebergs IF, called him to run 400 metres in a club dual meet and he did well despite an almost complete lack of training; realizing his potential, he started training seriously under coach Jan "Bobby" Strandberg and developed rapidly.
[1][3] The time was a new Swedish record; Josjö never improved it again, and it lasted until Jimisola Laursen ran 45.54 twenty years later.
[4] Josjö was selected to represent Europe at the 1981 IAAF World Cup in Rome in the 4 × 400 metres relay; the European team of Josjö, Fons Brijdenbach, Koen Gijsbers and Hartmut Weber placed second behind the United States.
[3] At the 1982 European Championships in Athens he represented Sweden in both the individual 400 metres and the 4 × 400 metres relay; in the individual event he was eliminated in the heats, while the Swedish relay team qualified for the final and placed eighth.
[8] At the 1984 Summer Olympics in Los Angeles Josjö competed only in the relay; Sweden qualified from the heats on time, but was eliminated in the semi-finals.