A source told ESPN.com Kuba's deal is worth $11.1 million for three years, and also includes a no-trade clause.
Kuba, who would have become an unrestricted free agent July 1, had said he wanted to remain with the Senators.
Kuba, 32, was making $3 million this season. He has two goals and 27 assists in 54 games with the Senators, his first year with the team.
Pierre LeBrun covers the NHL for ESPN.com. Information from The Associated Press was used in this report.