He was born in Buffalo, New York. His mother, Margaret (née Doyle), was a native of Killeagh, County Cork.
In the early years of his career Olcott sang in minstrel shows, before studying singing in London during the 1880s.
Olcott combined the roles of tenor, actor, lyricist and composer in many productions. He wrote the complete scores to Irish musicals such as Sweet Inniscara (1897), A Romance of Athlone (1899)
He was a good songwriter who captured the mood of his Irish-American audience by combining melodic and rhythmic phrases from traditional Irish music with melancholy sentiment. Some numbers from his musicals became popular, such as "My Wild Irish Rose" from A Romance of Athlone.
