In 1769 he was appointed assistant to Joseph Fownes (1715–1789) as minister of High Street Chapel, Shrewsbury.
On 29 December (elected 17 November) 1771 he succeeded Joseph Mottershead at Cross Street Chapel, Manchester.
From the institution of the Manchester Academy (22 February 1786) till 1789 Harrison was professor of classics and belles-lettres there.
Harrison published: Hymn tunes composed: Posthumous was Soon after settling in Manchester, he married Ann, daughter of John Touchet.
His son William (d. 30 Nov. 1859, aged 80) was minister at Blackley, Lancashire (1803–54); another son, John, (1786–1853), was a Manchester merchant and father of John Harrison, Ph.D. (d. 1866), minister at Chowbent, Lancashire (1838–47), Brixton, Surrey (1847–61), and Ipswich (1861–3).