In his first speech as prime minister outside number 10 Downing Street, 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.
"As I have travelled round the country and as I have listened... I have heard the need for change: change in our National Health Service, change in our schools, change with affordable housing, change to build trust in government, change to protect and extend the British way of life."
"On this day I remember words that have stayed with me since my childhood and which matter a great deal to me today: my school motto - 'I will try my utmost,' this is my promise to all of the people of Britain.
"And now let the work of change begin."
Later during the day, Blair was named as envoy for the Quartet group of Middle East negotiators.
Soon after being confirmed as the Middle East envoy, Blair resigned as a member of parliament.
Blair and Brown entered parliament together in 1983, once shared an office and were the chief architects behind the restyling of Labour, but their friendship soured as Brown believed Blair had reneged on a deal to hand over the leadership sooner.
Blair became prime minister in 1997 after Labour won the biggest parliamentary majority for half a century with a strong public mandate for change.
But his popularity ratings dropped considerably, partly because of his decision to join the US-led invasion of Iraq in 2003 and support for the so-called "war on terror".
In an interview with The Sun newspaper published on Wednesday, George Bush, the US president, rejected the allegation that Blair was an uncritical "poodle" to the US.
"He's bigger than that. This is just background noise, a distraction from big things. This kind of thing is just silly ridicule and that's how I treat it," he said.
At his final appearance in parliament, Blair was asked what he would do if he was given the role as Middle East envoy with the Quartet.
"Blair has been made a scapegoat for British foreign policy regarding Iraq"
Baton Rouge, US
Send us your views
"The absolute priority is to try to give effect to
what is now the consensus across the international community - that the only way of bringing stability and peace to the Middle East is a two-state solution," he said.
He said a Palestinian state would need to be "not merely viable in terms of its territory but in terms of its institutions and governance".
Members of the Quartet - the United States, United Nations, European Union and Russia - met in Jerusalem on Tuesday to discuss the appointment for which Blair was the only candidate.
Source: Al Jazeera and agencies