The team is to begin work on Monday. Activists say Syrian forces killed more than 300 people in several suburbs east and west of the capital on Wednesday.
A US official accused Damascus earlier of an “indiscriminate use of chemical weapons”. He said the delay was meant to allow evidence to degrade.
Syria has blamed “terrorists”.
State media have reported that chemical agents have been found in tunnels used by rebel fighters, and also that soldiers “suffered from cases of suffocation” when rebels used poison gas “as a last resort” after government forces made “big gains” in the suburb of Jobar.
‘Degradation of evidence’
The Syrian foreign ministry statement broadcast on state television said an agreement to allow UN chemical weapons experts to “investigate allegations of chemical weapons use in Damascus province” had been concluded on Sunday with the UN’s disarmament chief, Angela Kane.
The agreement was “effective immediately”, the statement added.
A spokesperson for UN Secretary General Ban Ki-moon subsequently announced that the inspectors were “preparing to conduct on-site fact-finding activities”, starting on Monday. A ceasefire will be observed at the affected locations, the statement said.
Russia, a key ally of Syria, welcomed the decision to allow UN inspectors in but warned the West against pre-empting the results.
“We strongly urge those who, by attempting to impose their own results on the UN experts, are raising the possibility of a military operation in Syria to use their common sense and refrain from committing a tragic mistake,” the Russian foreign ministry said.
Earlier, a senior US government official accused the Syrian authorities of intentionally delaying the UN probe “in order to facilitate the degradation of evidence of their use of chemical weapons”.
“Any belated decision by the regime to grant access to the UN team would be considered too late to be credible, including because the evidence available has been significantly corrupted as a result of the regime’s persistent shelling and other intentional actions over the last five days,” the official told reporters in Washington.
“Based on the reported number of victims, reported symptoms of those who were killed or injured, witness accounts, and other facts gathered by open sources, the US intelligence community, and international partners, there is very little doubt at this point that a chemical weapon was used by the Syrian regime against civilians in this incident.”
Medecins Sans Frontieres (MSF) said on Saturday that three hospitals it supports in the Damascus area had treated about 3,600 patients with “neurotoxic symptoms” early on Wednesday morning, of whom 355 died.
While MSF said it could not “scientifically confirm” the use of chemical weapons, staff at the hospitals described a large number of patients arriving in the space of less than three hours with symptoms including convulsions, pin-point pupils and breathing problems.
On Saturday evening, Mr Obama and UK Prime Minister David Cameron agreed that “significant use of chemical weapons would merit a serious response from the international community”, a Downing Street said.
Later, Syria’s Information Minister, Omran Zoabi, warned that US military action in Syria would not be a “walk in the park”.
“The military intervention in Syria has proved to be a weak case because Syria is still a strong state. It has institutions, an army,” he added. “It has friends and allies in the region.”
“If the US leads a military intervention, this will have dangerous consequences. It will bring chaos and the region will burn.”
The deputy chief of staff of Iran’s armed forces, Gen Massoud Jazayeri, also warned that there would be “severe consequences” if the US crossed what he called a “red line” on Syria.
A year ago, President Obama said that any attempt by Syria to use its chemical weapons would be a “red line” for the US, and change his administration’s “calculus” in the region.
In his first broadcast interview since fleeing Syria, former foreign ministry spokesman Jihad Makdissi told the BBC on Sunday that that launching missiles would solve nothing and only escalate the conflict.
“If it is used by the regime, it is suicidal; if it is used by fanatical groups, it is also criminal. So we have to end this insanity and give hope for Syrians to say that yes, we can gain something through dialogue,” he said.
The head of a Sunni jihadist rebel group, the al-Nusra Front, meanwhile promised to target President Assad’s minority Alawite sect in revenge for Wednesday’s attack.
“For every chemical rocket that had fallen on our people in Damascus, one of their villages will, by the will of God, pay for it,” Abu Mohammed al-Golani said in the recording posted online.