Follett was born at Topsham in Devon, the eldest son (of ten children) of Captain Benjamin Follett, late 13th Regiment of Infantry, who had retired from the army in 1790 and gone into business as a timber merchant, and his wife Ann Webb, daughter of John Webb, of Kinsale, Ireland. His younger brother was Brent Spencer Follett (1810-1887) QC, MP.
Follett received his education at Exeter grammar school and Trinity College, Cambridge, graduating in 1818. Follett entered the Inner Temple in 1816 and began to practise as a pleader below the bar in 1821, was called to the bar in 1824, and joined the western circuit in 1825. In 1835 he was returned to parliament for Exeter. In parliament he rapidly distinguished himself, and under the first administration of Sir Robert Peel he was appointed in November 1834 as Solicitor-General. He resigned with the ministry in April 1835. In the course of this year he was knighted. On the return of Peel to power in 1841 Follett was again appointed Solicitor-General, and in April 1844 he succeeded Sir Frederick Pollock as Attorney-General.
His health began to fail him in 1838, and he was permanently injured by a severe illness in 1841. In 1845 his health broke down, and he was compelled to relinquish legal practice and to visit the south of Europe to recuperate. He returned to England in March 1845, but the tuberculosis, with which he had previously been diagnosed, reasserted itself and he died in London on 28 June 1845. He was buried in the Temple Church in London.