Reily was born in Sedalia, Missouri, but moved to Fort Worth, Texas as a teenager where he worked both in the newspaper and real estate businesses. During this time, he first became active in local politics and was appointed as the chairman of the Republican City Committee and the Republican County Committee, as well as being twice nominated for County Clerk. In 1892, Reily went to Kansas City and was appointed as the Secretary to the Mayor for two terms. Following that, he returned to private life, but was subsequently appointed as Chief Deputy to the County Assessor. In 1902, he was appointed as the Assistant Postmaster for Kansas City. In 1901, Reily founded the Roosevelt Club, which had a stated goal of nominating Vice President Theodore Roosevelt for President in the 1904 elections. The group was disbanded when Roosevelt became President after the assassination of William McKinley in September of that year. As a newspaper editor in Kansas City, Reily was said to be the first prominent figure to endorse Warren G. Harding for the office of President of the United States. When Harding was elected President in 1920, he is said to have sought an appointive office to which he could nominate Reily as a reward for his loyalty, without giving him too much power or presence in Washington.
On July 30, 1921, President Harding nominated Reily as Governor of Puerto Rico. During his time in office, he was a strong supporter of "Americanism", the introduction of some aspects of mainland United States culture and their advancement over native Puerto Rican culture. During his inauguration address, he insisted that the United States flag should be the only flag used over the island. Additionally, he placed several mainland politicians in prominent positions in the Puerto Rican government. Although Reily was a strong proponent of "Americanism", he reportedly saw Spanish culture—such as that of Texas, Florida, and California—to be part of this culture. During his term as governor, Spanish Renaissance Revival became the "official" architectural style of the territory for public buildings and the new Puerto Rico Capitol Building was erected in that style. During his time in office, Reily advocated reducing the use of Spanish in schools in favor of teaching exclusively in English. Reily was an extremely unpopular governor. A common nickname for him, given by the Puerto Rican populace, was "Moncho Reyes", a name closely resembling Reily's and giving the impression that Reily was an uncivilized. He became involved in disputes with numerous political factions in Puerto Rico, some of which called for his removal from office. Reily reported, in a letter to Harding, that he had received death threats. He was also the subject of corruption allegations and an investigation by Puerto Rican local officials. Under pressure to leave office, and suffering from an illness he had contracted during a return visit to the continental United States, Reily resigned as governor on March 1923. He was succeeded by U.S. RepresentativeHorace Mann Towner, the Chairman of the House Committee on Insular Affairs, which had jurisdiction over Puerto Rico. A collection of original correspondence between Reily and President Harding is archived in the Manuscripts Division of the New York Public Library.