He attended private schools, including Phillips School and Brooks School. He graduated from Harvard University in 1872 and from Harvard Law School in 1875.
He was admitted to the Suffolk bar and commenced practice in Boston. and served in the Massachusetts State Senate. He also served as Boston commissioner of parks. He was an unsuccessful Democratic candidate for Governor in 1886.
Andrew was elected as a Democrat to the Fifty-first and Fifty-second Congresses (March 4, 1889 – March 3, 1893).
He served as chairman of the United States. House Committee on Reform in the Civil Service (Fifty-second Congress). He was an unsuccessful candidate for reelection in 1892 to the Fifty-third Congress.
Andrew resumed the practice of his profession, and died in Boston on May 30, 1895. His interment was in Mount Auburn Cemetery in Cambridge.
He was a member of the Massachusetts House of Representatives.