[1] Ternström worked in the Swedish General Export Association (Sveriges allmänna exportförening) from 1948 to 1957 before becoming an attaché at the Ministry for Foreign Affairs in 1957.
Ternström was deputy head of the Administration Department at the Foreign Ministry in 1973.
He was ambassador in Tunis in 1976 and served in the Swedish United Nations delegation in New York City in 1978.
[1] In 1981, while Ternström was ambassador in Egypt, he escaped unhurt after the Egyptian President Anwar Sadat was assassinated.
[4] Ternström worked as a special adviser to Oxfam from 1993 to 1994 and correspondent for Svenska Dagbladet from 1994.