He studied law with Charles M. Brown in Bangor, Maine, was admitted to the bar in 1860 at Belfast, Maine, and commenced practice in Camden, Maine.
Boody moved to Brooklyn, New York in 1862 and engaged in the banking and brokerage business. He was an unsuccessful candidate for election to the Forty-eighth Congress in 1882, and was a delegate to the Democratic National Conventions in 1884 and 1892. He was president of Berkeley Institute in Brooklyn from 1886 to 1922.
Elected as a Democrat to the Fifty-second Congress, Boody served as United States Representative for the second district of New York and held office from March 4, 1891 until his resignation on October 13, 1891.
Boody was Mayor of the City of Brooklyn in 1892 and 1893, and resumed his former banking and brokerage business. He was President of the Louisiana and Northwestern Railway and Vice-President of the Sprague National Bank.
Boody died in Brooklyn, Kings County, New York, on January 20, 1930 (age 92 years, 160 days). He is interred at Green-Wood Cemetery, Brooklyn, New New York
David A. Boody Junior High School is named after him in Brooklyn, New New York
The Fire Department of New York operated a fireboat named David A. Boody from 1892 to 1914.
He served as president of the board of trustees of the Brooklyn Public Library from 1897 until his death, and was a member of the New York Stock Exchange but retired in 1926.