Prime minister is first western leader to visit Burma since Aung San Suu Kyi's success in parliamentary byelections. Follow live coverage of their meeting here
The Press Association has more on Cameron's meeting with the Burmese president, Thein Sein, in the country's new capital Naypyidaw, which replaced Rangoon in 2005.
The two leaders met at Sein's palace. Thein told Cameron through a translator: "This visit of your excellency is significant and historical in our bilateral relations. We are very encouraged and we are most appreciative of your kind acknowledgement towards Myanmar."
Speaking on the tarmac as he arrived in Naypyidaw, Cameron said:
This country really matters. For decades it has suffered under a brutal dictatorship. It is also desperately poor. It doesn't have to be this way. There is a government now that says it is committed to reform, that has started to take steps, and I think it is right to encourage those steps.
The prime minister also said he wanted to meet opposition leader Aung San Suu Kyi, describing her as "a shining example for people who yearn for freedom, for democracy, for progress". He added: "We should be under no illusion about what a long way there is to go."
He said the government had to demonstrate that moves to democracy were "irreversible".
Cameron also said developments in Burma may be "one potential chapter of light" in a "world where there are many dark chapters in history being written".
Of course we should be sceptical. Of course we should be questioning. Of course we shouldn't be naive. Aung San Suu Kyi herself, who has spent so many years in such a long, lonely but powerful struggle, believes that he [Thein] is acting in good faith.
Britain had played a "leading role" in the imposition of sanctions, and would also not be "backwards" in responding to positive changes, he added.
He said it was "also right" to meet Aung San Suu Kyi, "who has shown incredible courage over these past decades and frankly is a shining example to people all the world who yearn for freedom, for democracy, for progress".
We should be under no illusions about what a long way there is to go and how much more the [Burmese] government has to do to show this reform is real and it is irreversible. We should be very cautious and very sceptical about that. We need to see progress on political reform. We need to see prisoners freed and changes that show the reform is irreversible.
The prime minister's convoy drove from the airport of the purpose-built capital down deserted roads. At one point it passed by a group of people who sprayed it with water to mark the Thingyan Burmese water festival.
Good morning. David Cameron has arrived in Burma, becoming the first western leader to visit the country since Aung San Suu Kyi's recent success in a series of parliamentary byelections.
This morning in the capital, Naypyidaw, Cameron met the Burmese president, Thein Sein, who faced down conservatives to allow Aung San Suu Kyi's National League for Democracy to contest the recent elections.
And at 10.30am the British prime minister is due to meet Aung San Suu Kyi in Rangoon.
In a speech yesterday in Indonesia Cameron, who is on a whistle-stop tour of the region, paid tribute to both the president and the opposition leader.
The prime minister's visit to Burma is likely to have an immediate impact as it accelerates moves towards the scaling-down of sanctions against the country.
Cameron yesterday gave his strongest hint yet that Britain would take the lead in pressing for a relaxation of EU sanctions and expressed the hope that the recent political reforms would be irreversible.
The prime minister said:
What I see happening in Burma is a potential flowering of freedom and democracy and I think that from everything I've seen – although I will see for myself tomorrow – it seems as if the president of Burma is intent on taking a new path and wants to see a progressive flourishing of freedom and democracy …
I hope that following my meetings tomorrow I will have the confidence to go back to my country, to back to others in the European Union, and argue that the change in Burma is irreversible, that they are set on a path towards democracy, that in a world of difficulty and darkness and all sorts of problems, here is one bright light that we should encourage, and we should respond in a way that makes that regime feel that it is moving in the right direction and that the world is on its side.
Britain was, until recently, in the lead in demanding sanctions remain in place. Cameron is now believed to be planning to argue in favour of an immediate change when foreign ministers meet in Brussels on 23 April, barring any diplomatic disaster in Burma today, reports my colleague Nicholas Watt, who is accompanying the PM on his Asian tour. Cameron's visit to Burma is his last stop.
We will be covering events live here throughout the day. Cameron is due to meet Aung San Suu Kyi at around 10.30am, followed by statements to the press at 11.30am.