He was educated at the Edinburgh Academy and Edinburgh University, graduating in medicine in 1864.
After entering Middle Temple as a student in 1865, Finlay was called to the bar two years later and built up a successful practice, becoming a Queen"s Counsel in 1882. He lost his seat in 1892 but regained it three years later, the same year he was appointed Solicitor General and knighted. In 1900, Finlay became Attorney General for England and Wales and also became President of the Edinburgh Sir Walter Scott Club, and gave the Toast to Sir Walter at the club"s annual dinner.
In 1902 he was elected Lord Rector of Edinburgh University.
Foreign his services in representing the British Empire in a number of international legal arbitrations he was appointed Knight Grand Cross of the Order of Street Michael and Street George in 1904, and the following year became a Privy Counsellor. However, in the 1906 general election he again lost his seat, and it was to be another four years before he returned to Parliament as representative for Edinburgh and Street Andrews Universities.
In 1916, Finlay became Lord Chancellor in Lloyd George"s coalition government, being at the same time created Baron Finlay, of Nairn in the County of Nairn. He sat on the Woolsack for three years, and in 1919, on his retirement, was created Viscount Finlay, of Nairn in the County of Nairn.
Lord Finlay married Mary, daughter of Cosmo Innes, in 1874.
She died in June 1911. Lord Finlay died in March 1929, aged 86, at his home in Kensington, London, and was buried at Nairn.
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Three years later he was elected Liberal Member of Parliament for the Inverness Burghs, but broke with William Ewart Gladstone over Irish Home Rule and joined the Liberal Unionists in 1886.
The following year he was appointed a British member of the Court of Arbitration at The Hague, and in 1921 was elected a Judge of the Permanent Court of International Justice established by the League of Nations.