Each player would have become an unrestricted free agent July 1.
Neuvirth, 28, said earlier Wednesday he was hoping to remain with the Flyers.
"There's a great group of guys here," he said. "Love the city, love the organization. Trying to do whatever I can to be here."
Neuvirth is in the final season of a two-year, $3.25 million contract (AAV of $1.625 million), according to CapFriendly.com. He's 10-9-1 with a 2.90 goals-against average and .887 save percentage in 24 games this season.
Neuvirth, selected by the Washington Capitals in the second round (No. 34) of the 2006 NHL Draft, is 94-80-22 with a 2.68 GAA, a .911 save percentage and 10 shutouts in 224 games in nine seasons with the Flyers, New York Islanders, Buffalo Sabres and Capitals.
Bellemare, 31, has six points (three goals, thee assists) in 62 games and leads the Flyers in average shorthanded ice time per game at 2:54. He said negotiations began last week.
"I'm really proud and happy the Flyers wanted to negotiate to keep me," he said. "It's a boost of confidence. … I wasn't expecting anything to be settled this early in the year. I'm really happy that my way to work, I can have six points and that didn't stop them from believing in me. I'm going to make them not regret it. I'm going to make them proud for sure."
Bellemare was signed by the Flyers on June 11, 2014. He has 32 points (16 goals, 16 assists) in 217 games in three NHL seasons.