"They were both single and started dating recently," a source close to the new couple told People on Monday.
"It's just the beginning stages of a relationship and they're having a great time," the source added.
"They are totally hot for each other," another source told US Weekly.
Cuoco is obviously a fan of Cavill's film work. The actress tweeted a photo of herself alongside a "Man of Steel" poster last month.
Everyone go see "man of steel". It's fantastic in every single way. pic.twitter.com/8MHv41zrQS— Kaley Cuoco (@KaleyCuoco) June 15, 2013
"It was a wonderful relationship but we never spoke a word about it and never went anywhere together," the actress told CBS Watch! magazine.