Welch was born on December 4, 1835, in Milton Township, Wayne County, Ohio.
Following the outbreak of the American Civil War, he enlisted with the 2nd Ohio Cavalry of the Union Army and would reach the rank of lieutenant colonel.
Other positions Welch held include Postmaster of Westfield Township, Medina County, Ohio, in 1861.
In January 1900, Welch was appointed cashier in the office of the Sergeant-at-arms of the United States House of Representatives, Henry Casson.
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