William Otto entered the University of Pennsylvania in 1829, receiving his degree of A. B. in 1833. After that he studied law in the office of Joseph R. Ingersoll.
William Otto moved to Brownstown, Indiana, in the fall of 1836. In 1844 he was elected president judge of the second judicial circuit. He was the last judge to be elected by the legislature and served until 1852, when he was defeated by George A. Bicknell, Democrat. For five years, 1847-52, he was professor of law at Indiana University. At thirty-six, he had won the reputation of being one of the ablest presiding circuit judges in the state. On the bench he was autocratic and austere, brooking no familiarity, but outside of official life he displayed a sense of humor and a pleasing personality. At the expiration of his term in 1853, he moved to New Albany and engaged in private practice. His services were at once in demand for cases pending in the Indiana Supreme Court. In 1855 he was employed to test the constitutionality of the state liquor law as counsel for the appellant in Beebe vs. the State. In the decision a substantial part of the law was adjudged unconstitutional.
In 1858 Otto was defeated as Republican candidate for the state attorney-generalship. In 1860 he was one of the Indiana delegates to the Republican National Convention. From the first he supported Lincoln and in January 1863 Lincoln appointed him assistant secretary of the interior. In this position he took an active interest in Indian affairs and recommended legislation for Indian betterment. His ability gained him the respect of Orville H. Browning and Hugh McCulloch, who urged Grant to appoint him arbitrator for the United States under the convention with Spain for the adjudication of claims for damages sustained by American citizens in Cuba. He resigned as assistant secretary of the interior in 1871 to accept this position and served until 1875 when he was appointed reporter of the United States Supreme Court.
Meanwhile Otto continued with his law practice, and in January 1873 he argued before the United States Supreme Court on the Judiciary Act of February 5, 1867, maintaining that the Supreme Court, under this act, had no more power than under the Act of 1789 even though the express limitation of powers had been omitted. The decision, given two years later, upheld Otto's arguments. In 1883 Otto resigned as Supreme Court Reporter, having completed seventeen volumes of reports. In 1885 he was appointed one of the United States Representatives to the International Postal Congress at Lisbon. After his retirement from public life he continued to practise law. He died in Philadelphia in his ninetieth year.
William Otto was a member of the Republican National Convention from Indiana in 1860.
Otto never married, but a tombstone erected by him in the cemetery at Brownstown marks the grave of a woman who was to have become his wife.