A Sudanese diplomat has said the force should be made up of 3,000 men, with Sudan and Chad each providing 1,500.
Prior to his Khartoum visit, Deby said last week: "I am a man of dialogue and openess. War has never settled things... Chad wants to live in perfect harmony with all its neighbours."
Improved ties between the two countries is seen as a major step towards peace in Darfur, the province in western Sudan where at least 300,000 people have died, according to UN estimates, since ethnic tensions escalated and led to a revolt in 2003.
Scott Gration, the US envoy, said: "We are extremely grateful for both the Sudanese government and the Chadian government to reach out to each other.
"We think this is historic, but more than that we think this is an absolute key to breaking what we think is a cycle of insecurity that is going on in Darfur," he said.
Sudan accused Chad of backing Darfur-based rebels of launching a suprise attack on Khartoum, the Sudanese capital, in May 2008.
Chad denied involvement and responded with an accusation that Khartoum backed rebels who attacked the Chadian capital, N'Djamena, in February that year.
Deby took power in a military coup in 1990, with Sudan's backing. Eastern Chad currently hosts thousands of Sudanese refugees who fled the civil war in Darfur.