Waters was born Joyce Mary Partridge in Auckland on 2 June 1931, the daughter of Mary Elizabeth Partridge (née Harrison) and Thomas Harold Charles Partridge. She was educated at Diocesan School for Girls, Auckland, from 1938 to 1949, and went on to study at Auckland University College, graduating Bachelor of Science in 1954, Master of Science with first-class honours in 1955, and PhD in 1960. The title of her doctoral thesis, supervised by John Llewellyn and David Hall, was A study of some co-ordination compounds formed between nickel diammines and the nitrite ion. She was the second woman to complete a PhD in chemistry at Auckland.
In 1959, she married fellow inorganic chemist Neil Waters, who was knighted in 1995.