The deal represents an expansion of the relationship with the Foyt squad, with which Hildebrand drove in last year's Indianapolis 500.
He will compete in the #11 Chevrolet entry which Tatiana Calderon is driving on road and street courses in 2022.
It will be the first time since 2017, when he was full-time with Ed Carpenter Racing, that Hildebrand has entered any more than the Indianapolis 500 in a single season.
“I'm excited to have this opportunity to get back in the car, do a little more racing, and work with the AJ Foyt Racing squad again,” he said.
“Although the results may not have looked special on paper, I was really impressed by what we accomplished last year at the 500 and look forward to attacking these other ovals on the IndyCar schedule alongside Kyle [Kirkwood] and Dalton [Kellett].”
The 34-year-old American finished second as an Indianapolis 500 rookie in 2011, having led until he crashed at the very last corner while lapping a backmarker and was overtaken by Dan Wheldon.
Last year, he qualified 22nd and finished 15th, best of the four drivers whom AJ Foyt fielded in the event.
“We had a great experience working with JR last year, and there is no doubt he is very competitive at Indianapolis,” said team president Larry Foyt.
“He is still very motivated to drive IndyCars and is a set-up-savvy, technical driver who will be a strong addition at our oval races this year.”