Keen was educated at The King's School, Rochester and Dollar Academy, and graduated LLB (with Honours) in law from the University of Edinburgh in 1976, where he was a Beckman scholar.

In 2016, he appeared for the United Kingdom Government in the R (Miller) v Secretary of State for Exiting the European Union ("Article 50 case") where he successfully argued that there was no constitutional requirement for the devolved administrations to consent to Brexit.

He remained Dean until January 2014 when he resigned to become chair of the Scottish Conservative Party, having been chosen in November 2013 to succeed David Mundell MP.

[citation needed] On 16 September 2020, Keen offered his resignation over the United Kingdom Internal Market Bill, stating that he found it difficult to reconcile parts of it with the law.

[14] In 2017, Keen was charged with contravening section two of the Firearms Act 1968 by failing to safely secure a shotgun,[15] to which he pleaded guilty and was fined the sum of £1,000.