The BBC's political editor Nick Robinson said the paper had timed its decision for maximum political impact.
While it was unwelcome for Mr Brown, he did not expect the Sun to be as vocal in its criticism of the prime minister as it had been of Labour leader Neil Kinnock in 1992 when the paper claimed to have swayed the outcome of the election.
Former Labour deputy leader Margaret Beckett said the Sun's switch was a "problem" for the party but not "insurmountable".
George Pascoe-Watson, the Sun's political editor, said it had given Labour "one last chance" in 2005 but now felt it was time for a new government.
"The prime minister failed to convince us he was the right man for the country," he said.
The Scottish edition of the Sun has not endorsed the Conservatives.
In response, Mr Brown said he did not "get out of bed" each morning thinking what the newspapers were saying about him.
"In the end we would would like the support of every newspaper, you'd like to have the support of lots of people that are not giving you support. but it is people that decide elections," he told the Today programme.
He said he believed Sun readers would back new policies on tackling anti-social behaviour and on cancer test guarantees which he said appealed to the "mainstream, middle" of British society.
Mr Brown said he had "set out a vision for a more responsible society and for a more accountable politics" in Tuesday's speech.
New proposals, such as free home care for 300,000 most at-need pensioners, were "properly costed", he insisted.
He also defended the new focus on anti-social behaviour and measures against the most "chaotic families" in society, saying it was time to be "more explicit about the responsibilities we demand of our citizens and the boundaries between right and wrong".
Asked about whether he would take part in a series of TV debates with Tory leader David Cameron, Mr Brown said he had made up his mind but now was not the time to discuss the issue.
While admitting that Labour "had a lot to do to persuade the British people" to elect them for a historic fourth term, he said he "relished" the challenge of fighting the Tories.
Conservative Party Chairman Eric Pickles said the party's head of communications, Andy Coulson, had brought him the "good news" on Tuesday evening.
However, he denied the Sun's move was linked to the Tories' decision to appoint Mr Coulson - a former editor of The News of the World, the Sun's sister paper - as a senior aide.
"It is more about how Gordon Brown's government is failing to deliver for the British people and the sense of direction and vision that David Cameron is offering," he told the BBC.
The Sun remains Britain's top-selling newspaper
The Sun was a big supporter of Margaret Thatcher, backing the controversial poll tax and mounting attacks on Tory MPs who plotted against the then-prime minister.
After she was ousted in 1990, the Sun stood by her successor John Major, and on polling day in 1992, the paper ran a front page showing Labour leader Neil Kinnock's head in a light bulb.
The headline read: "If Kinnock wins today, will the last person to leave Britain please turn out the lights."
Many pundits had predicted a Labour victory but the Tories retained power, prompting the Sun to famously declare: "It's The Sun Wot Won It."
However, Prof David Denver, from the University of Lancaster, said the influence of newspapers on voters was "hugely exaggerated".
"Newspapers are only a secondary source of information and a poor secondary source of political information at that. It's television that counts," he told the BBC.
"It's much more likely that papers shift to bring themselves in line with their readers rather than they influence their readers in a particular direction."
In 1992, the Sun sold more than 3.5 million copies a day. It is still the UK's top-selling newspaper, with average daily sales of 3.13 million in August, according to the Audit Bureau of Circulation.
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