Swiss television viewers chose the Christian missionary group’s rock tune from among five national finalists.
The Eurovision contest is a kitschy fixture on the European cultural calendar watched by more than 100 million people across the world.
Viewers and juries pick the winner from an eclectic mix of bubblegum pop and rock acts representing each European country.
Political songs are forbidden and Swiss media have speculated that the Salvation Army’s Christian aims might still fall afoul of the rules.
Switzerland hasn’t won the contest since Canadian singer Celine Dion represented the country in 1988.