Newton Webster Finley, lawyer and judge, son of Rev. Robert S. and Mary H. (Cole) Finley, was born in Lauderdale County, Mississippi, on July 31, 1854, and his family moved to Texas later that year. Finley had four brothers, one of whom was Richard Watson Finley, and three sisters. He was educated in the common schools of Marshall, Jefferson, and Daingerfield and heard law lectures from Gen. Thomas J. Jennings in Tyler. In June 1876 Finley was admitted to the bar by district judge William H. Bonner at Quitman. He entered practice at Tyler that year. Until 1885 he worked in a partnership, Chilton, Robertson, and Finley, in Smith County. Afterwards he formed a partnership with Marsh and Butler that lasted until he moved to Dallas in 1893.
Finley served as a Democratic presidential elector in 1884. He was chosen state chairman of the Democratic party of Texas in 1888 and was reelected to that position in 1891. He organized the Car Stable Convention, which renominated James Stephen Hogg for governor. Governor Hogg appointed Finley associate justice of the new Court of Civil Appeals of the Fifth Supreme District in Dallas in 1893. The Democrats nominated Finley for the same position in 1894, and he was elected. Governor Charles A. Culberson appointed him chief justice of the same court in 1897. He was elected to that position the following year and retained it until April 1900, when he resigned to practice law in Dallas. He was head of Finley, Harris, Ethridge, and Knight, a firm that later became Finley, Knight, and Harris. In 1907 Governor Thomas M. Campbell appointed Judge Finley a member of the board of regents of the University of Texas, a position he held until his death.
Finley was a member of the Masons, the International Order of Odd Fellows, and the Knights of Pythias. He was also a member of the Trinity Methodist Church in Dallas. He was chairman of the board of stewards of the church and president of the Methodist Laymen's Council of Dallas from its inception. He was active in the building of Trinity Church. In June 1877 he married Alma Louise Woldert of Tyler. They had two daughters. After Mrs. Finley died in 1883, he married Minnie Lee Simms of Fort Worth in 1886. They had four children. Finley died of pneumonia on September 23, 1909, in his home in Dallas and was buried in Greenwood Cemetery.