Alvord was born on March 11, 1844 in Greenfield, Massachusetts. He served as Professor of Agriculture of the Massachusetts Agricultural College from 1886 to 1887, as well as the second president of Oklahoma Agricultural and Mechanical College from 1894 to 1895. He became interested in the emerging western cattle industry while serving as a cavalry officer in the United States Army, and Alvord later lobbied for the passage of the Hatch Act of 1887 and the Morrill Act of 1890, which helped establish agricultural experiment stations. He died on October 1, 1904 in St. Louis, Missouri while attending the World's Fair.