He was born in Riga. Most of his career he played with the Riga Jewish community sports club Hakoah. In the Latvia national football team he made his debut in 1935 against Lithuania and in the debut match he scored two goals.
In his 23 matches for Latvia Vestermans scored 13 goals. It was the third result in goals for Latvia players before World War II, however Vestermans achieved it in significantly fewer matches than Ēriks Pētersons and Alberts Šeibelis who had a better goal-tally. Vestermans was considered one of the most talented footballers in Latvia. Vestermans left Latvia before Latvia was annexed by the Soviet Union and until his death at the age of 90 he lived in Florida, United States.