Analysis of information sources in references of the Wikipedia article "3rd millennium BC" in English language version.
Both the dromedary (the one-humped camel of Arabia) and the Bactrian camel (the two-humped camel of Central Asia) had been domesticated since before 2000 BC.
As has already been mentioned, this type of utilization [camels pulling wagons] goes back to the earliest known period of two-humped camel domestication in the third millennium BC.