Gonchar and the Stars have since agreed to a two-year, $10 million contract.
The native of Chelyabinsk, Russia, had received an offer from a team in the KHL, but has decided to stay in the NHL.
Gonchar, 39, registered three goals and 24 assists for 27 points in 45 games with the Senators this season.
In 1,177 career NHL regular-season games, to date, with the Washington Capitals, Boston Bruins, Pittsburgh Penguins and Senators, Gonchar has accumulated 217 goals and 558 assists for 775 points.
TSN's Darren Dreger first reported the deal via Twitter.