The deal is worth $25.5 million, ESPN.com's Pierre LeBrun reported.
The Sabres announced the signing Wednesday after players reported for physicals. Hodgson was already in Buffalo and was expected to be present for the team's first practice Thursday.
He is a four-year NHL player who was a restricted free agent after the Sabres retained his rights by offering him a qualifying tender in June.
Hodgson centered Buffalo's top line last season and finished second on the team with 15 goals and 34 points in 48 games.
The Sabres acquired Hodgson in a trade with Vancouver in February 2012. Overall, he has 35 goals and 77 points in 139 career games.
Information from ESPN.com's Pierre LeBrun and The Associated Press was used in this report.