Robinson was born at Newby Hall, Yorkshire, the second son of Thomas Robinson, 2nd Baron Grantham, and his wife, Lady Mary, née Yorke, daughter of the second Earl of Hardwicke. He was educated at a preparatory school at Sunbury-on-Thames, and, from 1796 to 1799, at Harrow followed by St John's College, Cambridge from 1799 to 1802. william Pitt the Younger was Member of Parliament for Cambridge University, to which, as The Times said, "accordingly most of the budding Tory statesmen of the day resorted". Robinson was an accomplished classicist, winning Sir william Browne's Medal for the best Latin ode in 1801. After graduating in 1802 he was admitted to Lincoln's Inn. He remained a member there until 1809, but did not pursue a legal career and was not called to the bar.

Against the background of the Napoleonic Wars Robinson did part-time military Service at home as Captain (1803), ultimately Major (1814–17) in the Northern Regiment of West Riding Yeomanry.

Robinson entered politics through a family connection. His mother's cousin, the third Earl of Hardwicke, Lord Lieutenant of Ireland, appointed him as his private secretary in 1804. Two years later Hardwicke secured for him the parliamentary seat of Carlow, a pocket borough near Dublin. In 1807 Robinson gave up the seat and was elected as MP for Ripon, close to his family home in Yorkshire.

In his first years in Parliament Robinson declined offers of junior ministerial posts, out of deference to his patron Hardwicke, who was an opponent of the Prime Minister, the Duke of Portland. However, the Foreign Secretary, George Canning, chose him as the secretary of Lord Pembroke's mission to Vienna, aimed at securing a new treaty of alliance between Britain and Austria. The mission was unsuccessful, but Robinson's reputation was not damaged, and, as his biographer E Royston Pike puts it, "as a good Tory [he was] given several small appointments in successive ministries." His political thinking was greatly influenced by Canning, but he became the protégé of Canning's rival Lord Castlereagh, who appointed him his under-secretary at the War Office in May 1809. When Castlereagh resigned from the government in October, unwilling to serve under the new Prime Minister, Spencer Perceval, Robinson resigned with him. In June 1810 he accepted office as a member of the Admiralty board. At the time of Perceval's assassination early in 1812, he was absent from parliament ostensibly on militia duties in Yorkshire.

Robinson served under Lord Liverpool as Vice-President of the Board of Trade between 1812 and 1818, and as joint-Paymaster of the Forces between 1813 and 1817, from which position he sponsored the Corn Laws of 1815. Robinson's Corn Importation Bill, successfully presented to Parliament in February 1815, was a protectionist measure, imposing minimum prices for imported wheat and other grains. The Historian Gregor Dallas writes:

In 1814 Robinson married Lady Sarah Albinia Louisa Hobart (1793–1867), daughter of the 4th Earl of Buckinghamshire, and first cousin to Castlereagh's wife. There were three children of the marriage, only one of whom survived to adulthood:

In 1818 Robinson entered the cabinet as President of the Board of Trade and Treasurer of the Navy, under the premiership of Lord Liverpool. In 1823 he succeeded Nicholas Vansittart as Chancellor of the Exchequer. The Historian Richard Helmstadter writes:

Canning's health had been declining since the beginning of 1827, and on 8 August he died. A prominent Whig commented, "God has declared against us. He is manifestly for the tories, and I fear the king also, which is much worse." The King, however, though he had long inclined to favour Tories over Whigs, was still angry at the refusal of Wellington and Peel to serve in Canning's cabinet. A widespread expectation (possibly shared by Wellington himself) that the King would send for Wellington was confounded. On the day of Canning's death Goderich and the Home Secretary, william Sturges Bourne, were summoned to Windsor Castle, where the King announced his intention of appointing Goderich to the premiership.

Wellington was by now distancing himself from the ultra-Tory wing of his party, and by January 1828 the King had concluded that the coalition could not continue and that a Tory ministry under Wellington would be preferable. Goderich had already written a letter of resignation to the King, but had not yet sent it, when he was summoned to Windsor. He described the disintegrating state of his administration; the King asked him to send for the Lord Chancellor, who was in turn bidden to summon Wellington to receive the King's commission to form a government. According to one account, Goderich was in tears during his interview with the King, who passed him a handkerchief, but within days Goderich was rejoicing in his release from office: "quite another man [who] sleeps at nights now, and laughs and talks as usual." His premiership had lasted 144 days, which was then, and at 2015 remains, the second shortest in British history, three days longer than that of his immediate predecessor, Canning.

Apart from his political career Goderich served as President of the Royal Geographical Society from 1830 to 1833, and of the Royal Society of Literature from 1834 to 1845.

In 1833 Goderich was created Earl of Ripon. He had not sought the advancement in the peerage, but wished to accept the King's offer of the Garter, for which, at that time, a viscountcy was considered an insufficient rank. He left the Colonial Office in the same year, and did not wish to hold any further office, but Grey insisted on his taking the senior non-departmental post of Lord Privy Seal. However, the next year Goderich and Stanley broke with the Whigs over what they saw as a threat to the established status of the Church of Ireland.

From 1841 to 1843 Ripon served in Peel's second administration as President of the Board of Trade, with the young W. E. Gladstone as his deputy. His final ministerial post was President of the Board of Control from 1843 to 1846. During his career, as Helmstadter observes, he had been, in succession, "a Pittite, a Tory, a Canningite, a Whig, a Stanleyite, a Conservative, and a Peelite. Between 1818 and 1846 he was a member of every government except Wellington's and Melbourne's."

Ripon died at Putney Heath, London, in January 1859, aged 76. He was succeeded by his only son, George who became a noted Liberal statesman and cabinet minister and was created Marquess of Ripon. The son was unique in being conceived at No 11 Downing Street, while Robinson was Chancellor of the Exchequer, and being born at No 10, when his father, now Goderich, was Prime Minister.

Robinson served as Chancellor for four years, and was regarded as a success in the post. The public finances were in good order, with a revenue surplus for the first three years of his chancellorship. He cut taxes and made grants to house the Royal Library in the British Museum and to buy the Angerstein collection for the National Gallery. Jupp writes, "These achievements, together with his support for Catholic relief and the abolition of slavery, led to his being regarded as one of the most liberal members of the government and to two more nicknames – 'Prosperity Robinson' and 'Goody'." Robinson's last year at the Treasury was overshadowed by a run on the banks, caused by the collapse of the City of London Bankers Pole Thornton and Co. Robinson was not blamed for the collapse, but his measures to mitigate the crisis were widely seen as half-hearted.

Goderich is 'the man with the hat' in the painting "The Staircase of the London Residence of the Painter" by the Dutch Painter Pieter Christoffel Wonder. In 2014 a Dutch art student did research on the painting and discovered that it depicts the resignation of Prime Minister Frederick John Robinson in January 1828. The research can be found on the Academia.edu website.