He studied law with Asa Hascall, a Malone attorney and Politician who served as town supervisor, justice of the peace, district attorney, and member of the New York State Assembly. Wheeler was admitted to the bar in 1845, and practiced in Malone. He was District Attorney of Franklin County from 1846 to 1849. He was a member of the Assembly (Franklin Co.) in 1850 and 1851; and of the New York State Senate (17th D.) in 1858 and 1859.
He was elected as a Republican to the 37th United States Congress, holding office from March 4, 1861, to March 3, 1863. He was elected to the 41st, 42nd, 43rd and 44th United States Congresses, holding office from March 4, 1869, to March 3, 1877.
William Almon Wheeler was born in Malone, New York, and attended Franklin Academy and the University of Vermont, although monetary concerns forced him to drop out without graduating. (Wheeler received the honorary degrees of master of arts from Dartmouth College in 1865 and LL.D. from the University of Vermont (1867) and Union College (1877). In 1876 he received his bachelor of arts degree from the University of Vermont "as in course", making him a graduate of the class of 1842.
When Congress voted a pay raise in 1873 and made it retroactive for five years (the Salary Grab Act), Wheeler not only voted against the raise, but after it passed he returned his salary increase to the Treasury department.
Wheeler was considered a "safe" choice for the vice presidential nomination, as he had not made many enemies over the course of his political career, though Roscoe Conkling himself supported the former congressman from New York Stewart L. Woodford. When the time came for the convention to nominate a vice-presidential candidate, congressman Luke P. Poland of Vermont nominated Wheeler, who immediately surged to the lead over Woodford and several other candidates. By the time the roll call reached New York, the result was apparent, and Woodford withdrew, enabling New York to cast all its votes for Wheeler. Wheeler won the nomination with 366 votes to the 89 for his nearest rival Frederick T. Frelinghuysen, who later served on the Electoral Commission which decided the 1876 election in favor of Hayes and Wheeler.
He was inaugurated in March 4, 1877 and served until March 4, 1881.
Hayes had announced at the start of his administration that he would not run for a second term. Wheeler did not run for the 1880 Republican presidential nomination, and retired at the end of his term.
He retired to Malone in March 1881 when his term as vice President was over. In May 1881, Platt and Roscoe Conkling resigned their U.S. Senate seats in a dispute with President James A. Garfield over control of patronage in New York, triggering two special elections. In the legislative election for Platt's seat, it took six weeks of balloting to elect a candidate; Wheeler's name was in consideration, and he received as many as 23 votes before Warner Miller was elected with 76 votes on the 46th ballot.
Wheeler died at his home in Malone, New York at 10:10 A.M on Friday, June 4, 1887, 26 days before his 68th birthday. The funeral was held at the Congregational church in Malone. He was interred next to his wife in Malone's Morningside Cemetery on June 7, 1887.
During his House tenure, Wheeler served as chairman of the Committee on Pacific Railroads (42nd Congress) and the Committee on Commerce (43rd Congress).
Wheeler was also a candidate for Conkling's seat; the voting went on for several weeks, and he received as many as 50 votes in earlier ballots before Elbridge G. Lapham won with 92 votes on the 56th ballot.