Björck was born on 19 September 1944 in Nässjö, Sweden, the son of Arne Björck and his wife Ann-Marie (née Svensson). He attended Centralskolan in Nässjö and passed studentexamen at Nässjö läroverk in 1966. Swedish was interested in politics from an early stage. He was national chairman of the Moderate Youth League, or the Rightist Youth League (Högerns ungdomsförbund) as it was known at the time of his election. He was the first truly young – only 21 – chairman of the Youth League – his predecessor was 35 years old. Before that he served as national chairman of the Conservative School Youth, today known as the Moderate School Youth, from 1961 to 1963.
