Jennings and Foakes haven't played for England since the West Indies tour 12 months ago, but impressed in the 3-0 series whitewash of Sri Lanka in November 2018.
Jennings made his highest test score, 146, and Foakes was player of the series in scoring 277 runs at an average of more than 69.
Foakes' inclusion meant there was no room for Bairstow, with national selector Ed Smith saying he needed a rest after playing in three formats for England "without a significant break."
James Anderson, England's record wicket-taker, missed out as he recovers from a cracked rib sustained in the 3-1 series win in South Africa while fellow paceman Jofra Archer had already been ruled out because of an elbow injury.
Offspinner Moeen Ali remained unavailable for selection, Smith said.
The first test is in Galle from March 19-23 and the second in Colombo from March 27-31.
England: Dominic Bess, Stuart Broad, Jos Buttler, Zak Crawley, Sam Curran, Joe Denly, Ben Foakes, Keaton Jennings, Jack Leach, Matthew Parkinson, Ollie Pope, Joe Root (captain), Dominic Sibley, Ben Stokes, Chris Woakes, Mark Wood.