He was born in a rural area in Doddridge County, West Virginia on November 9, 1874. He attended Salem College of West Virginia, now Salem International University but did not earn a degree. At the outbreak of the Spanish-American War he entered the United States Army as a private. Following the war, he earned a law degree from West Virginia University.

He entered the practice of law in Fairmont, West Virginia and was elected its mayor in 1908. He was elected as a Congressman to an unexpired term in 1913 and was re-elected through 1918. In the 1920 election, he was defeated, due to his association with the policies of Woodrow Wilson.

He then ran for, and was elected to, the United States Senate in 1922 as a Democrat. He was defeated for re-election in 1928. He then ran for the state's other Senate seat in 1930 and was elected. He was re-elected in 1936. In 1940 he ran for governor and resigned the remaining two years of his Senate term.

He soon regretted his decision and strongly considered resigning to run for his old Senate seat in 1942. In later life he expressed strong regret for his term as governor. Upon the expiration of his term as governor in 1944, he ran for and was elected to his old House seat. He was, however defeated for re-election in 1946.

In 1948 he was again elected to the Senate, beginning his third non-consecutive term there. He continued to serve until his death in 1958.

He was an ardent segregationist. He sought out the chairmanship of the U.S. Senate Committee on the District of Columbia, where he opposed any actions to change the racial status quo there, or to provide basic services to the residents of the District.

Neely was known through his political career as a master orator. In his honor, Fairmont State University sponsors an oratory contest in his name every year.