Billeter was born in Sierre, Switzerland. He was trained as a draftsman in Basel, where he first began to publish poetry. He co-founded a Literary magazine, Sphaira, which published 1962-1964.
Billeter emigrated to Australia in 1966.. He settled in Sydney, where he worked as a draftsman, and began contributing to Australian magazines. He published his only collection of poetry in 1973. In 1974 he and John Jenkins founded the [[literary magazine etymspheres. In 1977 he edited the anthology3 Blind Mice with Kris Hemensley and Robert Kenney.