Keenan was born in Perth. His father Peter was born in County Durham, England. During the parliamentary eligibility crisis of 2017, it came to public attention that Keenan had acquired British citizenship by descent at birth, which he renounced before the 2004 election. Some media outlets had incorrectly reported that he had never renounced his citizenship; in response, he wrote "I am an Australian citizen and I do not hold citizenship of any other country. Fairfax is aware of this, yet in a cheap grab for a headline they have ignored this". Keenan went to school at Trinity College, Perth. He later attended Murdoch University, the Australian National University, and Cambridge University, where he obtained a master's degree in philosophy. He was a property consultant with a real estate firm before entering politics. He had previously worked as an adviser to Senator Amanda Vanstone and was deputy director of the Liberal Party of Western Australia.
Following the 2013 federal election, Keenan was appointed Minister for Justice in the Abbott Government. He was also made Minister Assisting the Prime Minister on Counter-Terrorism in May 2015. In the 2015 leadership spill, Keenan was again identified as one of Turnbull's supporters. He retained both his positions in the new ministry. During the 2016 federal election campaign, Keenan was accused of starting a smear campaign against the Muslim Labor candidate Anne Aly, in reference to her previous counter-terrorism work. Keenan appeared with Liberal MP Luke Simpkins, the incumbent in Cowan whose seat was challenged by Aly, to make accusations against her. However, prior to Aly becoming a Labor candidate, Simpkins had written to her in admiration of her counter-terrorism work. As justice minister, Keenan oversaw the first national firearms amnesty since the 1996 Port Arthur massacre. It ran from July to September 2017, allowing people to hand in unregistered or unwanted firearms. The amnesty had been approved in March 2017 by the Firearms and Weapons Policy Working Group to reduce the number of unregistered firearms in Australia that were being used in Islamic terrorist attacks. In a ministerial reshuffle in December 2017, Keenan was promoted to cabinet as Minister for Human Services and Minister Assisting the Prime Minister for Digital Transformation. On 25 January 2019 he announced that he would not contest the 2019 election to spend more time with his family, after 15 years in parliament. He and his wife have four sons born while he was a member of parliament. On Wednesday 13 February 2019, one of Keenan's office staffers was implicated in conspiring with Michaelia Cash's office staff in making strategic media leaks about AFP raids on the offices of the AWU.
