His father, also Richard Yates, was also an Illinois politician; indeed the senior Yates was Illinois' popular Civil War governor, and the younger Yates spent a portion of his boyhood living in the Executive Mansion in Springfield, which would one day again be his home. The son was born in Jacksonville, Illinois and attended public schools and, from 1870 to 1874, the Illinois Woman's College (now MacMurray College). He was the city Editor of the Daily Courier in 1878 and 1879, and of the Daily Journal 1881–1883. Yates graduated from Illinois College in Jacksonville in 1880 and from the law department of the University of Michigan at Ann Arbor in 1884. He practiced law in Jacksonville and was city attorney of Jacksonville 1885–1890 and county judge of Morgan County 1894–1897. From 1897 to 1900 Yates was United States collector of internal revenue for the eighth internal revenue district.
Yates served as a private in Company I, Fifth Infantry, Illinois National Guard from 1885 to 1890.
In 1900, Yates was elected governor in his own right, at not yet 40 years of age. He began his campaign in a "dark horse" capacity under the cloak of neutrality, which won him support from Senator Shelby Moore Cullom's "federal crowd". Congressman william Lorimer, who had backed another candidate in a field of well-known men, suddenly switched at the Republican convention, grabbing up a Yates banner and proceeding to stampede the convention. This played out with the results of the third ballot never being announced; Yates was then nominated on the fourth. The subsequent election, decisive, sent Yates to the governor's chair, by 61,233 votes over Democrat Samuel Alschuler of Aurora.
Yates, despite being a sitting governor, did not receive his party's nomination in 1904; he led the field of six candidates for 58 ballots, before throwing support behind State's Attorney Charles S. Deneen, in order to prevent the nomination of Frank O. Lowden, Yates' chief rival at the convention. In his years prior to Congress, Yates was popular on the chautauqua circuit, as well as working patronage jobs, such as serving in charge of telephone companies, as a member of the state utility commission.
His final act of Service was to cast a vote in 1933, against repeal of the 18th Amendment (Prohibition). After leaving Congress, Yates resided in Harbor Springs, Michigan, and Springfield, Illinois, while writing his memoirs. He died in Springfield and was buried in Diamond Grove Cemetery, Jacksonville.