The Typhoons were launched from RAF Coningsby in Lincolnshire to identify an "unresponsive civilian aircraft", the RAF said.
Communications were re-established and the aircraft was safely escorted to Cardiff Airport, a spokesman added.
The Challenger 300 jet left the airport at 19:20 GMT, thought to be heading to its original destination, Dublin.
Cardiff Airport said the plane had temporarily lost radio contact.
"As a precautionary measure the aircraft was escorted into Cardiff Airport as a safe place to land," it said.
The airport added that it was open and operating as normal.
It is understood that one passenger and two crew were on board the private jet.
All the main emergency services sent crews to Cardiff Airport at about 16:30 BST, including seven fire appliances. Police and ambulance also attended.
The sonic boom caused by the RAF jets was heard across Oxfordshire.
Two RAF jets were scrambled to escort a private plane into Cardiff airport after it lost radio contact.