The Australian-born doctor and his wife, Evelyn, began work in 1953 on their natural family planning system at the invitation of the Catholic Marriage Guidance Bureau.
Marian Corkill, director of the Ovulation Method Research and Reference Centre of Australia, said, "He changed the understanding of fertility though the work that he has done."
The Billings Method has been effective in assisting couples both to avoid and achieve pregnancy, especially for those who had been considered infertile, through an enhanced understanding of women's ovulation cycle.
"Most notably in the past decade, the Billings Ovulation Method has been successfully introduced into China, where it is now the only government-approved method of natural family planning," Corkill said in a statement.
Billings is survived by his wife and eight of their nine children.