The flood of refugees has exacerbated existing internal conflicts in the two countries.
According to figures from the UN there are about 400,000 Sudanese refugees and displaced Chadians in Chad and 200,000 displaced people in the Central African Republic.
The resolution authorises the EU, under chapter seven of the UN charter, which allows the use of military force, to deploy a force for one year in eastern Chad and northeastern Central African Republic.
The force will help improve security, facilitate the delivery of humanitarian aid, and "contribute to protecting civilians in danger, particularly refugees and displaced persons".
The resolution also establishes a UN mission in both countries that will include international police, military liaison officers, and experts in human rights, civil affairs and the rule of law.
It will select and train a new unit of Chad's police to maintain law and order in refugee camps, key towns and areas with large numbers of displaced civilians in eastern Chad.
Idriss Deby, the president of Chad, originally opposed a proposal from Ban Ki-moon, the UN secretary general, for a UN military force but agreed to an EU presence after meeting Bernard Kouchner, the French foreign minister, in June.
EU defence ministers are expected on Friday to give a final go-ahead for the deployment of up to 4,000 troops by the end of the year beginning next month.
The UN would field up to 300 police, 50 military liaison officers and civilian personnel.
France is expected to supply the bulwark of the EU troops and has 3,000 air force personnel already stationed in Chad.
The EU force would complement a planned mission of up to 26,000 UN and African Union troops and police in Darfur itself.
Andrew Simmons, Al Jazeera’s Africa bureau chief, said the sheer size of Chad and the Central African Republic will make things difficult for any deployment.
"This is a major undertaking because these two countries are vast and both have their own problems aside from the spillover of refugees in Darfur," he said.
Both the Chadian and the Sudanese governments are accused of having supported each other's rebels, prompting attacks against Chadian villages.