Blair was greeted at the presidential palace in Khartoum by Vice-President Ali Usman Taha.
The two are scheduled to spend 45 minutes in talks before Blair meets President Umar al-Bashir.
His decision to intervene personally in the crisis, becoming the first serving British prime minister to visit an independent Sudan, was kept secret until the last moment for security reasons.
The prime minister is set to take a tough line, telling Sudanese leaders that the international community expects immediate changes in Darfur, the crisis-hit region of western Sudan.
Violence in Darfur has left an estimated 50,000 people dead and 1.4 million more displaced.
Before leaving London late on Tuesday at the start of an African mission, Blair's official spokesman said the prime minister's uncompromising message would be that Sudan "must comply" with United Nations resolutions on Darfur.
The Security Council has threatened sanctions against Sudan if it fails to take steps to disarm the Janjawid militias, held responsible for atrocities in Darfur.
The Darfur crisis erupted when the Sudanese government called on the militias to help subdue a revolt that broke out in February 2003, as mainly black African tribes rose up against the central government which they said had ignored their region's development.
While al-Bashir and others were sure to put up a robust counter-argument against Blair, legislators from Darfur added that former colonial ruler Britain had to bear some blame for the crisis.
About 1.4 million people have
been displaced by Darfur conflict
"The United Kingdom is responsible for what is happening now in Darfur because it was the country which found Darfur as a separate state and invaded it and annexed it to the rest of Sudan without preserving any of its constitutional rights," said Idris Yusuf Ahmad, who represents South Darfur.
Blair is to tell Sudan's leaders that they must negotiate a peace settlement with the rebels and fully accept the role of the African Union in keeping peace as well as assisting aid efforts, his spokesman said.
The United Nations World Food Programme (WFP), which is spending about $200 million this year providing emergency relief in Darfur, said on Wednesday that the situation remained "very, very precarious".
While more aid is getting through and humanitarian agencies are receiving more cooperation from the authorities, Blair and other world leaders have to make sure Darfur is not forgotten, WFP spokesman Greg Barrow said.
"The crisis is in the spotlight at the moment, and this helps us, but what we are saying is that this crisis is going to continue to the end of this year and then maybe for another," he said.
"The UK is responsible for what is happening now
in Darfur because it was the country which found Darfur as a separate state and invaded it and annexed it to the rest of Sudan without preserving any of its constitutional rights"
Idris Yusuf Ahmad,
South Darfur representative
With few crops planted in Darfur this year, millions would remain dependent on international aid, he explained.
Blair, who has pledged to make Africa one of his key policies during 2005, when Britain holds the rotating presidency of both the G8 rich nations' club and the European Union, is due to leave later on Wednesday for Ethiopia.
There he is to attend a two-day meeting of the Commission for Africa in Addis Ababa, his personal project designed to galvanise development efforts.