Henderson, 19, has been particularly impressive for the Black Cats in making 31 Premier League appearances this season, starting 21 games. Meyler, 20, has also featured on nine occasions under Steve Bruce.
"I have been delighted with the way Jordan and David have applied themselves since I arrived at the club, and credit has to go to the academy staff for the fantastic work they do with our young players," Bruce told the Sunderland Echo.
"You look for players to step up to the plate and make an impression when you first arrive and over the course of the last nine months, they have grasped the opportunity with both hands.
"It blazes a trail for the younger players at the club who can see there is a route into the first team if they apply themselves like Jordan and David have. We are delighted to have secured their services for another five years."