Amusingly, Brown used a quote very similar to anouther new PM, a Mr H. Saxon....Gordon Brown has become the UK's prime minister, succeeding Tony Blair.
Posing outside No 10 with wife Sarah, the man who has been Mr Blair's chancellor for the past 10 years, said: "Let the work of change begin."
He said his priorities were education, health and restoring trust in politics. He promised he would "try my utmost".
Outgoing PM Blair has stood down as an MP and taken up a new job as a Middle East peace envoy. He was earlier given an emotional standing ovation by MPs.
It is the first time in 17 years a UK prime minister has entered office without a general election.
Mr Brown said: "This will be a new government with new priorities. And I have been privileged to have been granted the great opportunity to serve my country.
"And at all times I will be strong in purpose, steadfast in will, resolute in action in the service of what matters to the British people, meeting the concerns and aspirations of our whole country."
Reshuffle
Mr Brown promised to lead a government of "all the talents" and said his "mission" was to provide "the best of chances for everyone".
"If we can fulfil the potential and realise the talents of all our people then I'm absolutely sure that Britain can be the great global success story of this century," he told reporters in Downing Street.
Then, quoting his school motto, he said: "I will try my utmost. This is my promise to all of the people of Britain. And now let the work of change begin."
Mr Brown is thought likely to carry out the bulk of his Cabinet reshuffle on Thursday, but it has already emerged that two definite changes will see Patricia Hewitt departing her role as health secretary and Margaret Beckett leaving her post of foreign secretary.
Blair job
Conservative leader David Cameron congratulated Mr Brown on becoming prime minister - but demanded he hold an immediate general election.
Speaking on his Webcameron internet site, the Tory leader said: "Gordon Brown doesn't have the mandate, he wasn't elected as prime minister, and he should go to the country."
Earlier, Mr Brown spent 57 minutes inside Buckingham Palace in a private audience with the Queen - more than double Mr Blair's 28 minutes.
Mr Brown, 56, becomes the 11th prime minister of the Queen's reign.
He has been seen as the unofficial prime-minister-in-waiting for the past decade - finally getting his chance when Mr Blair announced he would stand down after three terms.
He became Labour leader unopposed on Sunday after potential rivals had failed to gain enough support to mount a challenge.
Mr Blair is travelling by train to his Sedgefield constituency, in the North East of England, where he is expected to bid farewell to local party members after 24 years as their MP.
He will take up a new job as a peace envoy for the "quartet" of the UN, America, EU and Russia.
Earlier, as they left Downing Street the Blair family - including their four children - posed for the gathered world media.
Mr Blair said nothing to the press as they got in the car, but wife Cherie smiled and waved at the press and said she would not "miss" them.
In his final prime minister's questions in the Commons Mr Blair received a standing ovation from MPs on all sides, in unprecedented scenes.
Tributes
Mr Blair admitted he had "never pretended to be a great House of Commons man" but he paid tribute to the "noble" work of MPs and - in his final words to Parliament - said: "I wish everyone, friend or foe, well and that is that, the end."
Mr Blair, who was being watched from the public gallery by his family, also paid tribute to troops killed in Iraq, saying he was "truly sorry about the dangers they face today".
Conservative leader David Cameron hailed Mr Blair's "remarkable achievement" in being prime minister for 10 years, praising peace in Northern Ireland and Mr Blair's work in the developing world which he said will "endure".
He wished Mr Blair "every success for whatever he does in the future".
Mr Blair thanked Mr Cameron for his tributes and said although he could not wish the Tory leader well politically, "personally I wish both him and his family very well indeed".
Lib Dem leader Sir Menzies Campbell said that, despite their political disagreements, Mr Blair had been "unfailingly courteous" and extended his party's best wishes to the outgoing prime minister and his family.
Mr Blair returned the compliment, saying Sir Menzies had a "generosity of spirit and courtesy".
Story from BBC NEWS:
Oh, and if anyone wishes to know how the hell our system works. Go read the manual...or something.
