Childers was educated at Cheam School from 1836 to 1843, and the University of Cambridge, graduating with a degree in Mathematics in 1850. His public career began in Victoria, Australia in 1851, when he was appointed inspector of schools, then secretary to the education department and emigration agent for Melbourne. In 1852, he became auditor-general and a member of the legislative council. In 1853 Childers introduced a bill for the creation of the University of Melbourne and served as its first vice-chancellor. Later that year, he was appointed collector of customs, a post which gave him a seat on the executive council. In 1856, Childers was returned to the new parliament and served in the cabinet as commissioner of trades and customs.

In 1857 Childers removed to London as agent-general for Victoria, but the appointment was cancelled after a change of government. Childers next embarked upon a career in British politics and was elected as Liberal MP for Pontefract in 1860. He chaired a select committee on transportation and served on a royal commission examining penal servitude. In 1864 Childers was appointed a civil lord of the Admiralty and in the next year he became financial secretary to the Treasury under William Gladstone, who was chancellor of the exchequer. In 1867, Childers served on a royal commission reviewing the condition of the law courts.

Childers had become a firm supporter of Gladstone, who valued his ability. On the formation of Gladstone’s first administration in 1868, Childers was appointed first lord of the Admiralty. His tenure was marred by the capsizing of the iron-clad warship HMS ‘Captain’ on 7 September 1870. Childers' second son, Leonard, a midshipman, was among those who died. The accident sparked a violent controversy within the Admiralty over who was ultimately responsible and Childers resigned in March 1871. He returned to office in 1872 as chancellor of the duchy of Lancaster.

When Gladstone regained power in 1880, his confidence in Childers was demonstrated by appointment to a series of high offices. Childers became secretary of state for war in 1880. His tenure was noted for the Anglo-Transvaal War of 1881 and the Egyptian campaign of 1882. Childers reformed the army, which was reorganised on a territorial basis. In 1882, he was appointed chancellor of the exchequer. Childers was able to reduce taxation in his first budget of 1883-4, but by 1885-6, a heavy deficit and demands on the public finances created by crises abroad, required the introduction of a range of new taxes, which eventually led to the fall of the government in June 1885.

In Gladstone's short administration of 1886, Childers, now representing South Edinburgh, returned to the cabinet as home secretary. He supported Gladstone's first bill for home rule in Ireland. Although re-elected in 1886, ill health interrupted his political career, and Childers withdrew from politics in 1892.