His parents were Warren Green Currier (born in New York) and Deborah Heyliger of the Netherlands.

He joined the missionary order the Congregation of the Most Holy Redeemer (Redemptorists) in 1875 and was ordained a priest on November 24, 1880, in Amsterdam by Bishop Henry Schaap (vicar apostolic of Surinam).

In Rome, on July 6, 1913, he was consecrated by Cardinal Diomede Falconio, O.F.M., and assisted by Domenico Serafini, titular archbishop of Seleucia Pieria, and Donato Sbarretti, titular archbishop of Ephesus, bishop emeritus of Havana.

Bishop Currier knew Greek and Hebrew and was fluent in Latin, English, Dutch, Spanish, French, German, and Italian.

Bishop Currier died on September 23, 1918, on a train traveling from Waldorf, Maryland, to Baltimore to assist in the funeral of Cardinal John Murphy Farley, archbishop of the Archdiocese of New York.