Gonchar had 15 goals and 76 assists in 186 games over three seasons for the Senators. He led Ottawa defensemen in scoring with 27 points -- three goals and 24 assists -- this season, the last of a three-year, $16.5 million contract.
The 39-year-old Gonchar was set to become an unrestricted free agent July 5. However, he signed a two-year, $10 million contract with the Stars on Monday. TSN earlier reported the agreement Saturday.
Gonchar has 217 goals and 558 assists in 1,117 games over 18 seasons. The Russian spent his first nine seasons with Washington and also played for Boston and Pittsburgh.
Information from ESPN.com's Pierre LeBrun and The Associated Press was used in this report.