The deal is worth a total of $5.2 million, sources told ESPN.com's Pierre LeBrun.
The 31-year-old Ott, who was acquired in the Ryan Miller deal from Buffalo, had three assists and 37 penalty minutes in 23 regular-season games. In six playoff games, he added two assists and 14 penalty minutes.
Ott had been the Sabres captain before the trade on Feb. 28. He's an 11-year veteran and a former 2000 first-round pick of the Stars.
Information from The Associated Press was used in this report.