Redington, only son of Christopher Redington (1780–1825), a captain in the army, by Frances, only daughter of Henry Dowell of Cadiz, was born at Kilcornan, Oranmore, County Galway. He was educated at Oscott College and at Christ's College, Cambridge, but did not graduate. Devoting himself to politics, he represented Dundalk in parliament in the Liberal interest from 1837 to 1846.
On 11 July 1846 he was appointed under-secretary of state for Ireland, in 1847 a commissioner of national education, and ex officio an Irish poor-law commissioner. As a member of Sir John Burgoyne's relief commission in 1847 he rendered much active service during the famine, and in consequence of his services he was on 28 Aug. 1849 nominated a knight-commander of the civil division of the Bath, soon after Queen Victoria's first visit to Ireland. He served as secretary to the board of control from December 1852 to 1856, when he accepted the post of commissioner of inquiry respecting lunatic asylums in Ireland.
On 30 August 1842 he married Anne Eliza Mary, eldest daughter and coheiress of John Hyacinth Talbot, M.P., of Talbot Hall, County Wexford. He resided at Kilcornan House, but he died in London on 11 Oct. 1862.