Hökmark was born on 14 June 1920 in Malmö Karoli Parish, Malmöhus County,[1] the son of Anders Persson, a merchant, and his wife Clara (née Ahlgren).

[3] He graduated in 1942 and was commissioned as an officer the same year and was assigned as a second lieutenant to the South Scanian Infantry Regiment (I 7) in Ystad.

[2] From 1959 to 1960, Hökmark served as a company commander in the Swedish UN battalion, part of the United Nations Emergency Force (UNEF), in Gaza.

[2] Hökmark was promoted to major in Norrbotten Regiment in 1961 and served as Deputy Secretary in the 1960 Defense Management Investigation (1960 års försvarsledningsutredning) from 1961 to 1963.

He was promoted to lieutenant colonel in 1964 and was head of the General Department (Allmänna avdelningen) in the Defence Staff from 1963 to 1966 and expert in the 1964 Fortification Investigation (1964 års fortifikationsutredning) from 1964 to 1965.