Davis grew up in Ashtead, Surrey. He attended Dorking County Grammar School, which in 1976 became The Ashcombe School, Dorking and later studied Philosophy, Politics and Economics at St John's College, Oxford from 1981 to 1984, before obtaining an MPA at the Kennedy School of Government at Harvard University. While at Oxford University, Davis edited Cherwell, the student newspaper.

Davis began work as an economist at the Institute for Fiscal Studies, and while there he was briefly seconded to help officials work on early development of the Community Charge system of local government taxation (better known as the Poll Tax). In 1988 he moved to the London Business School, writing articles for their publication "Business Strategy Review". He returned to the Institute for Fiscal Studies in 1992, writing a paper on "Britain, Europe and the Square Mile" for the European Policy Forum which argued that British financial prosperity depended on being seen as a bridgehead to the European Union.

In 1993, Davis joined the BBC as an economics correspondent. He worked as economics editor on BBC Two's Newsnight programme from 1997 to 2001. In the mid-1990s he was a member of the Social Market Foundation's Advisory Council; he is a member of the British-American Project for a Successor Generation.

In 1998, Davis' book, Public Spending, was published by Penguin. In it he argued for the privatisation of public services as a means to increase efficiency.

While the BBC's economics editor, Davis was responsible for reporting and analysing economic developments on a range of programmes on BBC radio and television, particularly the Ten O'Clock News. He also had a role in shaping the extensive BBC coverage of economics across all the corporation's outputs, including online.

Davis also wrote a blog for the BBC website entitled Evanomics in which he "attempts to understand the real world, using the tool kit of economics". Subjects he discussed included road pricing, care for the elderly, Gordon Brown's Budget and how to choose wine.

Davis has won several awards including the Work Foundation's Broadcast Journalist of the Year award in 1998, 2001 and 2003, and the Harold Wincott Business Broadcaster of the Year award in 2002. In 2008, Davis was ranked first in the Independent on Sunday's "pink list" of the hundred most influential gay and lesbian figures in British society.

In 2005, he was one of a handful of BBC staff who crossed strike picket lines. BBC staff were striking over announced job cuts.

In summer 2007, Davis was a guest presenter on the Today Programme for two weeks. In April 2008 he stood down as BBC Economics Editor and joined the Today Programme as a full-time presenter, replacing Carolyn Quinn. He says that one of the best things about presenting on the radio is that "you can look things up on Wikipedia while on air".

On top of his duties at Today he also presents The Bottom Line, a weekly discussion programme on Radio 4 and Dragons' Den, the BBC Two business reality show.

Davis is a keen motorcyclist, and was seen riding a Yamaha R6 motorcycle in BBC2's The City Uncovered with Evan Davis. He is openly gay and lives with his partner Guillaume Baltz, a French landscape architect.