Bower's parents were Jewish refugees who fled Prague after the German occupation of Czechoslovakia in March 1939 and arrived in London later that same year. After attending the william Ellis School in Hampstead, Bower studied law at the London School of Economics, before working as a barrister for the National Council of Civil Liberties. In 1970, Bower joined the BBC as a researcher on the programme 24 Hours before becoming a reporter on Panorama. He was a Producer on Panorama from 1975 until 1987. He left the BBC in 1995. Bower is married to Veronica Wadley, former Editor of the London Evening Standard, and has four children.

Bower's second book was Klaus Barbie: The Butcher of Lyon (1984) which documented Klaus Barbie's war crimes during World War II as head of the Gestapo in Lyon, Germany and his post-war work for the American intelligence agency Counterintelligence Corps (CIC) and South American narcotics and arms dealers. Bower's book was serialised in The Times in September 1983. Neal Ascherson positively reviewed the book in The Observer in January 1984.

In 1987, Robert Maxwell responded to the publication of two unauthorised biographies of himself with numerous lawsuits, threats of legal action against individual booksellers, and the rapid publication of an authorised biography by Joe Haines, political Editor of the Mirror Group which Maxwell owned. Of the two unauthorised books, Maxwell: A Portrait of Power by Peter Thompson and Anthony Delano was withdrawn from sale and all unsold copies pulped after Maxwell successfully sued the publishers and authors for libel. The second book, Maxwell: The Outsider by Bower sold out in hardback but Maxwell prevented the paperback edition appearing, in part by buying the publishing company which held the paperback rights. Maxwell also filed a libel action against Bower and the hardback publishers, Aurum Press. Maxwell allowed this action to lapse in 1990 but only after Bower and Aurum had submitted a detailed defence of the book.

In 2000, Richard Branson sued Bower for libel over an article he had written for the London Evening Standard in 1999. Branson chose not to sue the paper, but its Editor, Max Hastings, agreed the newspaper would fund Bower's defence. Branson lost the case, and later expressed regret at bringing the action. Bower continues to write articles critical of Branson's Business affairs, and published biographies of him in 2000 and 2014.

In 2001, Bower published The Paymaster: Geoffrey Robinson, Maxwell and New Labour, a biography of the Labour MP Geoffrey Robinson. The book's evidence that Robinson had solicited a £200,000 Business contract from Robert Maxwell led to Robinson being suspended from Parliament for three weeks as he had not disclosed the matter to an inquiry some years previously. Robinson denied receiving the money in question from Maxwell and denied that he had sought to mislead Parliament.

In 2003, Bower won the william Hill Sports Book of the Year Award for Broken Dreams: Vanity, Greed and the Souring of British Football, an investigation into corruption in English football.

Bower's joint biography of Conrad Black and Barbara Amiel Conrad and Lady Black: Dancing on the Edge was published in November 2006. In February 2007, Black filed a libel suit in Toronto against Bower over the contents of the book. The suit was frozen when Black was convicted of fraud and imprisoned.

The Daily Express proprietor Richard Desmond brought a libel action against Bower over a passing reference in Dancing on the Edge. Desmond claimed that the book included an account of an incident that weakened his "super-tough" reputation as a businessman and was therefore defamatory. Bower denied libel on the grounds of the story being "substantially true". The action was heard in July 2009 and Desmond lost the case. An unauthorised biography by Bower of Richard Desmond, titled Rough Trader, was written and printed in 2006, but still awaits publication.

In 2011 Bower published a biography of the Formula One executive Bernie Ecclestone titled No Angel: The Secret Life of Bernie Ecclestone. Ecclestone cooperated with Bower in the writing of the book, facilitating introductions to people for Bower. Over lunch Ecclestone told Bower "You write what you like, provided it's more or less the truth, because I'm no angel". Ecclestone's quote provided the title for the book. Ecclestone became friends with Bower and would say to him "What can I do that's evil for you?"

Bower's biography of the music executive and entertainment impresario Simon Cowell, Sweet Revenge: The Intimate Life of Simon Cowell, was written with Cowell's co-operation and published in April 2012. Cowell later said that Ecclestone had advised him to co-operate with Bower. The title of the book refers to Cowell's relationship with fellow entertainment impresario Simon Fuller. Though Cowell had given Bower some 200 hours of access to him, Bower subsequently said that Cowell had tried to restrict his access to sources. Cowell contacted Bower after the book's publication to say that he had found it "a bit embarrassing", adding "you got things I didn't know you'd got." Bower has secured Cowell's co-operation for a planned sequel to the book.

Bower's book, Broken Vows – Tony Blair: The Tragedy of Power, was serialized in the Daily Mail and published in March 2016.