The couple were first spotted on a dinner date last month. On Saturday, the two were seen driving together in Los Angeles, sparking rumours of a potential romance between the pair.
A source has now confirmed to TMZ that Cooper and Lopez are romantically involved, though they are not yet officially a couple.
"They are definitely dating," the insider insisted.
Lopez filed for divorce from her husband Marc Anthony in July, while Cooper split from girlfriend Renée Zellweger in March of this year.
The Hangover star has reportedly been interested in the singer "for a while".