José da Costa Nunes was born in Candelária, Azores, to José da Costa Nunes and his wife Francisca Felizarda de Castro Nunes. He was baptised four days later, on 19 March 1880.
After studying at the seminary in Angra, Nunes went to Macau as a missionary on 4 June 1903, and was ordained to the priesthood on the following 26 July. He then did pastoral work and taught at Macau's seminary until 1906. Nunes was named Vicar general of Macau and Timor from 1906 to 1913, when he began missionary work in Timor. He became Vicar capitular of Macau on 21 February 1917.
He died in Rome at the age of 96. He was buried in the Campo Verano, but his remains, in accordance with his will, were later transferred to the church of Sant'Antonio dei Portoghesi. In his will, Nunes had also expressed his desire to be buried in the cemetery of Horta, next to his parents, if he died in Portugal.