Smiles and handshakes seal a first step towards peace
The first official US reaction came from Secretary of State Colin Powell.
"We are very pleased with the work done by the Afghan leaders themselves, but also the German Government," Mr Powell said. But he added: "Now the real work is ahead."
Representatives of many industrialised countries are now gathering in Berlin to discuss aid to rebuild Afghanistan.
"After all the years of war, terror, suffering and humiliation, Afghans now have concrete prospects for peace and for the future," Mr Schroeder told delegates in Bonn.
UN role praised
Russia's Deputy Foreign Minister, Alexander Losyukov, said the accord was "very positive", while UK Foreign Secretary Jack Straw described it as a "significant achievement" and French President Jacques Chirac called it "a very important step."
The foreign minister of Pakistan - once the Taleban's ally but now a supporter of the US-led campaign in Afghanistan - said his government was "delighted".
Iran - never a friend of the Taleban - also welcomed the accord.
But the BBC's William Reeve in Kabul says a sudden turnaround in regional meddling in Afghanistan's affairs is unlikely.
The country's neighbours, Pakistan, Iran and Russia, who sponsored civil conflict in Afghanistan, are unlikely to give up their influence easily.
Each of the three countries will be wary of some of the Afghan groups represented in the administration.
European Union External Affairs Commissioner Chris Patten paid tribute to Mr Brahimi and described the accord as "a crucial first political step."
Mr Brahimi himself thanked Burhannudin Rabbani, a former Afghan president and leader of the Northern Alliance which now controls the capital, Kabul, for his help in securing the agreement.
Mr Rabbani accepted that he would not lead the new administration.
But another Afghan faction leader, Gulbuddin Hekmatyar, was less understanding.
Mr Hekmatyar, loathed by many Afghans for bombarding Kabul with rockets during fierce factional fighting in the 1990s, was not invited to the Bonn talks.
"The Americans have imposed their solution in Afghanistan and that puts in doubt the legitimacy of the authority which will emerge from this conference," he said.
The former king - who also welcomed the deal - is to be given the largely symbolic role of presiding over a traditional assembly which is to choose a larger administration in six months.
Deal struck by exiles
Only a quarter of the Afghan delegates are returning from Bonn to their country.
The others are exiles who have not lived in Afghanistan for many years.
The BBC's developing world correspondent, David Loyn, said the Bonn talks were built on hope more than expectation, and many voices were left out of the deal.
It will now be up to the head of Afghanistan's new power-sharing council, Hamid Karzai - helped by Mr Brahimi and UN ground troops - to impose the agreement, bringing Afghanistan's numerous ethnic groups and warlords on board.