Reece was born on a farm near Butler, Tennessee. He attended Watauga Academy, Carson-Newman College, New York University, and the University of London. He was an assistant secretary and instructor in New York University in 1916 and 1917. During the First World War, he enlisted in May 1917 and served with the American Expeditionary Forces from October 1917 to July 1919; was decorated with the Distinguished Service Cross, Distinguished Service Medal, Purple Heart, and the French Croix de Guerre with Palm. He was director of the School of Business Administration of New York University in 1919 and 1920.
Reece was elected as a Republican to the Sixty-seventh and to the four succeeding Congresses (March 4, 1921 - March 3, 1931). He was an unsuccessful candidate for reelection in 1930 to the Seventy-second Congress. Reece was elected to the Seventy-third and to the six succeeding Congresses (March 4, 1933 - January 3, 1947), but he was not a candidate for renomination in 1946.
Reece served as a delegate to the Republican National Conventions in 1928, 1932, 1936, 1940, 1944, and 1948. He was also a lawyer, banker, and publisher. He was a member of the Board of Regents of the Smithsonian Institution in 1945 and 1946 and chairman of the Republican National Committee from 1946-1948.
Reece was an unsuccessful candidate for election to the United States Senate in 1948. He would be elected to the Eighty-second and to the five succeeding Congresses and served from January 3, 1951, until his death in Bethesda, Maryland. While in Congress, he served as chairman of the Special Committee on Tax Exempt Foundations (Eighty-third Congress)
Interment is in Monte Vista Burial Park, Johnson City, Tennessee.