Charvis, capped 84 times and unlucky to miss out on a Wales recall for Saturday's Six Nations Championship clash against France in Paris, joined the Dragons last summer and has delivered a succession of top-class performances.
Charvis said: "As a squad, we have a lot to offer, and I feel I can contribute for another season.
"We are looking to reach a level of success, and if I can play a small part in that, then I am delighted to pledge my future with the region."
Sweeney, who will provide fly-half cover on the Wales bench at Stade de France, had been linked with a move away from Rodney Parade after signing up with the Dragons three seasons ago.
But the 27-year-old said: "There is a good coaching and management staff and a great bunch of players, and I am confident we can be successful as a region on and off the field."