Morton was born in Shoreham, Addison County, Vermont. He was a clerk in a general store in Enfield, Massachusetts, taught school in Boscawen, New Hampshire, engaged in mercantile pursuits in Hanover, New Hampshire, moved to Boston, entered the dry-goods business in New York City and engaged in banking in New York City. He was an unsuccessful candidate for election in 1876 to the Forty-fifth Congress. He was appointed by President Rutherford B. Hayes as honorary commissioner to the Paris Exhibition of 1878.
Morton was elected as a Republican to the Forty-sixth and Forty-seventh Congresses, serving from March 4, 1879, until his resignation, effective March 21, 1881. He was United States Minister to France from 1881 to 1885, and elected Vice President of the United States on the Republican ticket with Benjamin Harrison, serving from March 4, 1889 to March 4, 1893. He was Governor of New York from 1895 to 1897. Following his public career, he became a real estate investor. He died in Rhinebeck, Dutchess County, New York. He was intered in the Rhinebeck Cemetery.