Swan was born and raised in Australia. He is Jewish. Swan is the son of physician, journalist, and radio and television broadcaster Norman Swan; his aunt and uncle are also Australian journalists. He attended the Sydney Grammar School in Darlinghurst, Sydney. In Australia, he entered the field of journalism in 2010. He then moved to the United States in 2014 for a yearlong fellowship with the American Political Science Association before returning to journalism in 2015 and remaining in the U.S.

As a member of the Sydney Morning Herald in the Canberra Press Gallery, Swan was presented with the Wallace Brown Award in 2014 for most outstanding young journalist. In 2016, Politico named Swan one of “16 Breakout Media Stars.” In 2020, The Jerusalem Post named Swan in its list of the world’s 50 most influential Jews.

Swan began his career as a national political reporter based in Canberra, Australia’s capital city, for Fairfax Media and as a political correspondent for The Sydney Morning Herald. He joined The Hill in August 2015 as part of their campaign team.

Swan became a national political reporter for Axios in December 2016. While at Axios, Swan broke several stories about the Trump administration. Former Washington Post journalist Ronald Kessler claimed in his 2018 book The Trump White House: Changing the Rules of the Game that Swan is among a handful of reporters to whom President Donald Trump feeds information, with instructions to attribute quotes to an unnamed White House official.

He married an American reporter Betsy Woodruff of Politico on September 14, 2019. On September 9, 2020, she announced the birth of their first child, Esther Jane Swan. He intends to become an American citizen.

In August 2020, Swan was praised by people on social media for the manner in which he had conducted an interview with President Trump. During the interview, Swan pointedly questioned and fact-checked numerous false, misleading, or bizarre statements as the President spoke them. Media columnist for The New York Times Ben Smith wrote that Swan’s was “perhaps the best interview of Mr. Trump’s term.”