He attended Mundell"s School in Edinburgh and then Glasgow University to study Law and graduated in 1751.
His birthplace is given as either Argyll or Edinburgh. An advocate from 1757, he was engaged in the Douglas peerage case from 1764 to 1769. He was appointed Solicitor General for Scotland in 1783 and Lord Advocate in 1784.
He was Lord President of the Court of Session and Lord Justice General from 1789 to 1808, where he sat as Lord Succoth.
On his resignation in 1808, he was created a baronet, and resided at Garscube, about four miles from Glasgow on the banks of the river Kelvin. There he engaged in the management of his estate, and the performance of his duties as a country gentleman.
Lord Cockburn says of him that "he lived like a patriarch in a house overflowing with company, beloved by troops of relations, and courted for his character and hospitality by many friends."
He was awarded an honorary doctorate (Doctor of Laws) from Glasgow University in 1784. He was elected Lord Rector of the University of Glasgow in 1799.
He died in 1823 aged eighty-nine years.
Ilay married Susan Mary Murray of Murrayfield, sister of Alexander Murray, Lord Henderland in 1766. She lived until 1815. Their son, Arthur Connell FRSE (Ilay"s grandson) was a famous chemist and discoverer of Connellite.
Director of the Highland Society (1784).
Faculty of Advocates. 16th Parliament of Great Britain]
He became Member of Parliament for Glasgow Burghs in the same year.