The US president sealed the deal in a 40-minute phone call to the Prime Minister at his holiday retreat in Cornwall.
The two leaders agreed that Syrian tyrant Bashar al-Assad was responsible for using chemical weapons against children.
Mr Obama and Mr Cameron will discuss the military options in the next few days.
They include missile strikes, disabling the Syrian air force or enforcing a no-fly zone across the country. A No.10 source said: "The significant use of chemical weapons would merit a serious response.
"The PM and the President are now looking at all the options."
But they ruled out sending in British and American ground troops.
The source said both leaders believe President Assad is deliberately trying to cover up the atrocity in the eastern suburbs of the capital Damascus on Wednesday that left up to 1,000 dead.
Assad forces were yesterday shelling the area of the nerve-gas attack to destroy evidence.
The source added: "It seems increasingly unlikely the United Nations investigators will be allowed to go there." That was despite requests from UN disarmament chief Angela Kane who was in Damascus yesterday to press for access.
A US battlegroup of three warships in the eastern Mediterranean has been strengthened by a fourth ready to strike Syria with cruise missiles.
President Obama met his national security team yesterday to discuss plans.
"That requires positioning our forces to carry out whatever options the president might choose," said US Defence Secretary Chuck Hagel. Even Iran yesterday conceded Syrians had been killed in chemical attacks but did not say who it thought was responsible.
Meanwhile the Assad regime tried to pin the blame for Wednesday's attack on opposition groups.
Syrian state TV claimed that soldiers patrolling in the Damascus suburb of Jobar had found chemical weapon agents in rebel tunnels.
Russia said the nerve-gas outrage may be the work of rebels trying to provoke international action.
But Foreign Secretary William Hague dismissed the claims.
France joined the UK yesterday in blaming Assad for the attack.
Foreign Minister Laurent Fabius said: "All the information indicates there was a chemical massacre near Damascus and Bashar al-Assad is responsible".
TV footage showing civilians - many of them children - dead or suffering the horrific symptoms of gas poisoning shocked the world.
Aid group Medecins Sans Frontieres said hospitals it supports treated 3,600 patients with "neurotoxic symptoms" and 355 died.
Hospital staff described patients arriving with nerve gas-style symptoms including convulsions, extreme salivation, contracted pupils and sight and respiratory problems.
British defence chiefs will meet foreign counterparts in Jordan tomorrow to discuss options.