The 43-year-old long-time bachelor said he and Petitgout will tie the knot sometime this summer, possibly at the family home in Hyannis Port, Mass., The Providence (R.I.) Journal reported.
A graduate of Pennsylvania State University, Petitgout has a 3-year-old daughter from a previous marriage.
She teaches history at the Northfield Community School in New Jersey.
Kennedy introduced Petitgout to Rhode Island lawmakers Monday, including Gov. Lincoln Chafee.
"My father spoke about his 'true compass' guiding him through his journey of life," Kennedy said, referring to the title of the late Sen. Edward M. Kennedy's biography. "I have found mine with Amy."