If you can read only one book about Barack Obama, read his own, first one. If you can read another, Renegade is not a bad place to pick up his story. Written even as the US presidential campaign was unfolding and then as Obama prepared to move into the White House, Wolffe's work was quickly done, it was published in the US in June, barely four months into the Obama presidency. Its virtues are also its faults. Renegade is sometimes shallower and less forensic than you'd like it to be, but it does well what it set out to do. "This is the making of a president," Wolffe writes, "witnessed from a front-row seat, as it unfolded from its first day to its last."

There's a reason why Renegade is no run-of-the-mill campaign chronicle: writing it was Obama's idea. He raised it in March 2008 with Wolffe, a British-born journalist who was covering Obama's campaign for the Democratic presidential nomination as a correspondent for Newsweek, where he was a colleague of mine. At first wary of the idea, Wolffe warmed to it and brought it up with Obama a couple of months later. Obama grinned broadly and said: "That's why I'm running for president. Because I have good ideas." The Obama-Wolffe bargain that emerged from that conversation is another of the book's trade-offs. Wolffe got remarkable access, but Obama got some indirect control over the project. The senator from Illinois acknowledged to Wolffe that as the next president ("I intend to win") he'd have to be "careful" about what he said.

Obama's co-operation was a big plus, but so too were Wolffe's skills as a reporter, as a write, and as the architect of the book's very sensible structure. Wolffe plainly knew what he didn't want to do. Renegade is not a "campaign book" lark in the manner of Timothy Crouse's The Boys on the Bus. Nor is it a mere sequel to Theodore White's long-running The Making of the President series. Wolffe knows that in the era of the internet and rolling news coverage, such facile accounts are better left to the likes of Newsweek (from which Wolffe has now departed) or any number of other media that can churn them out at warp speed. Wolffe's technique is to combine biography and reportage, to take milestones along the campaign trail and use them as portals into the character and make-up of the man behind the candidate.

Along the way, the reader gets an insider's tour of the travelling circus-cum-endurance test that is the 21st-century American presidential race, along with handy, if cursory, micro-bios of Obama's family as well as his handlers, advisers and mentors, many of whom went with him to the White House. This would be by no means sufficient if it were not for Wolffe's special access to Obama, his family and friends and the campaign team. The author had more than a dozen one-on-one interviews with the candidate, and any number of off-the-record conversations.

Dreams From My Father is a constant backdrop to Renegade, as anyone who reads both books will recognise, but Wolffe is careful not merely to regurgitate its content. There's a particularly good chapter in Renegade on Obama's "blackness". Obama's memoir is the story of his self-discovery, of his African roots and of his coming to terms with the fact that in America, though his mother was a white American and his father a black African, he would always be seen as black, period. Wolffe updates and re-examines the question of Obama's identity through the lens of the campaign. America being America, Obama's success as a politician was partly made possible by his ability to emphasise his non-threatening, mainstream strengths sometimes at the expense of his African-American roots, a strategy that, as Wolffe points out, irked some black American leaders. This is one of many reminders in Wolffe's book that Obama, though historically exceptional as the first black president of the United States, is anything but a renegade. "Renegade" might be Obama's Secret Service codename, but it is a somewhat inapt title for this book.

Touching on the race theme, Wolffe also gives us a through-the-keyhole look at how Hillary Clinton's campaign sought to use race and Obama's upbringing abroad against him. He cites early evidence of this from Clinton's senior strategist, Mark Penn. It's worth recalling, as Wolffe does, that in the autumn of 2007 "Obama was lagging behind Clinton by 24 points among black Democrats". According to Wolffe, Penn "identified what he called a 'lack of American roots' as a key weakness that could sink Obama". Wolffe quotes from a Penn memo: Obama's "roots to basic American values and culture are at best limited. I cannot imagine America electing a president during a war who is not at his centre fundamentally American in his thinking and in his values". Wolffe says Penn's advice was to use the word "American" as much as possible and to deploy the Stars and Stripes as often as possible during campaign appearances. (By April 2008, Penn had resigned from his high-level role in the Clinton campaign.)

As you make your way through Renegade, it becomes clear that there's empathy between Obama and Wolffe. In an afterword, the author spells out the connection between reporter and candidate: "I told [Obama] my family story in brief: how my mother was Moroccan and my father was British, a rare combination where I had grown up in England." "What you and I share," Obama said to Wolffe, "is an ability to cross lines." The book is better for the subtle bond between them, but also because Wolffe makes a point in Renegade of not crossing one line in particular: he remains the examiner and Obama the examined.

• Stryker McGuire is a contributing editor to Newsweek and editor of International Quarterly