It will be both men's second year at the Italian-based team, sister outfit to champions Red Bull.
"Both drivers have done a good job this season," said team principal Franz Tost in a statement ahead of Sunday's Abu Dhabi Grand Prix.
"Since the summer break, both drivers have scored more points and everyone in the team has been impressed with their maturity in terms of working with the engineers and their racecraft on track."
Vergne has scored 12 points from 17 races so far while Ricciardo has nine to his tally. Toro Rosso are ninth in the constructors' standings with three rounds left.
"There are big expectations for next year and I'm ready and willing to fulfil them," said Ricciardo.
"I feel I have been growing and developing as a driver and my approach to the technical side of the sport has also progressed this year."
Vergne, who has been backed by Red Bull from the early years of his career, recognised it had been a tough debut season but felt he had also learned a lot.
"I feel much stronger now and I know I have become a better driver over the course of the season," he added.
- Sports & Recreation
- Motor Racing
- Red Bull