He was born in Edinburgh on 30 November 1794, the son of Sir John Connell (1765-1831), Judge of the Admiralty Court and his wife, Margaret Campbell (daughter of Sir Ilay Campbell, Lord Succoth). His paternal grandfather was Arthur Connell, Lord Provost of Glasgow.
Connell was educated at the High School in Edinburgh and then trained to be an advocate, qualifying in 1817. He studied at Edinburgh, Glasgow and Oxford Universities. His interests moved from law to chemistry and from 1840 to 1856 he was Professor of Chemistry at St Andrews University.
He died in St Andrews on 31 October 1863. He is buried in Warriston Cemetery in Edinburgh behind the large red sandstone monument to Rev Peddie on the main east west path above the vaults. The grave is vandalised and the obelisk originally on the monument lies toppled to one side.
He married St James's, Westminster, London 1839 his cousin Elizabeth Camilla Connell (d.1899), s.p.
- Oxford Dictionary of National Biography: John Connell
- Philosophical Magazine, vol 31 (1847)
- "Archived copy" (PDF). Archived from the original (PDF) on 11 November 2017. Retrieved 11 November 2017.CS1 maint: archived copy as title (link)