Horne was educated at Lancing College (Fields House, 1991–1996) and at Sidney Sussex College, Cambridge where he studied classics, graduating in 2001. While at Cambridge he was a member of the Footlights.

He made his first appearance at the Edinburgh festival in 2000 with his show, "How To Avoid Huge Ships". His 2003 Edinburgh show, "Making Fish Laugh" was nominated for a Perrier newcomer award. In 2004 he won a Chortle Award for Best Breakthrough Act. His shows with Tim Key have been "Every Body Talks" and "When in Rome", both of which featured unusually extensive use of Microsoft PowerPoint for a comic act. Horne toured Roman towns of the UK with the "When in Rome" show in early 2006.

Horne married his wife Rachel, a BBC Business Journalist, on 1 January 2005. The couple have three sons.

Between 24 October 2006 and 24 October 2007 he worked alongside fellow Comedian Owen Powell, in an attempt to find a person from every nationality living in London. After a year's search, they finally managed to meet people from 189 of the UN's 192 countries, and hence suggested there is nobody in the capital from Tuvalu, Palau or the Marshall Islands.

As a solo performer, Horne then wrote and performed "Birdwatching" at the 2007 Edinburgh Festival and "Wordwatching" at the 2008 Edinburgh Festival. He signed a two-book deal with Virgin Publishing to write up both of these stories as books. The first, entitled Birdwatchingwatching, came out early in 2009. The second came out in early 2010. On 18 January 2007, Horne became the first ever Comedian to perform in Second Life for a feature on Sky News. In 2011 he compered "The Horne Section", a comedy variety show. "Alex Horne Presents The Horne Section" has run for three series on BBC Radio 4.

Horne appeared as a contestant on Countdown in August 2008, winning three matches before being defeated. He also won the inaugural Comedians' Countdown Competition held at the Edinburgh Festival in the same month, beating Mark Watson and Stephen Grant to lift the trophy.

Alex Horne also appeared in the TV show on BBC Three called Britain in Bed in 2011.

On 26 November 2012, Horne chaired Never Mind The Buzzcocks on BBC Two. His 'Horne Section' band performed behind him at various points during the quiz and performed songs about guests Louis Smith, Josh Widdicombe and Paloma Faith.

He appeared as a guest on The Matt Lucas Awards on 16 April 2013 where he won "The Bravest Guest" Award.

From 2015, Horne has served as co-host alongside Greg Davies in the Dave series Taskmaster, which he created. From 2017, Horne will also serve as co-host in the US remake of the show – which carries a shorter, but similar format to the UK series.