After attending Boston public schools, he studied law in the office of Charles F. Donnelly.

[1] In July 1886, Galvin was appointed by George M. Stearns to serve as the Assistant United States Attorney for the District of Massachusetts.

When Stearns resigned in September 1887, Galvin was chosen by President Grover Cleveland to succeed him as United States Attorney for the District of Massachusetts.

[1] In 1891 he was appointed by Governor William Russell to serve on the Charles River Improvement Commission, who named Galvin their chairman.

[1] The Commission's work led to the design initiatives of Charles Eliot, Arthur Shurcliff, and Guy Lowell.