Eames was the daughter of a lawyer in the international courts system. She studied voice for four years in Boston, then with Mathilde Marchesi (Marchesi de Castrone, Mathilde) in Paris. Selected by Charles Gounod to sing Juliette in his Roméo et Juliette, she was so successful in this debut at the Paris Opéra in 1889 that she was called on to repeat the performance many times.

In 1891, having left the Paris Opéra because of jealous intrigues involving Australian coloratura soprano Nellie Melba (Melba, Dame Nellie), Eames appeared for the first time with the Metropolitan Opera in New York City as Juliette. She remained a leading member of the company until her resignation in 1909. She was also popular in London during those years—especially performing in the roles of Tosca, Donna Anna and Donna Elvira (in Don Giovanni), and Aida. In 1911 she returned from a brief retirement to perform the roles of Desdemona and Tosca with the Boston Opera. She later made periodic concert tours, often with her husband, the American baritone Emilio Edoardo de Gogorza. Her autobiography, Some Memories and Reflections (1927), was published after her final retirement in 1916. From 1936 she lived in New York City, where she taught singing.