A person familiar with the contract revealed the terms of the deal. The person spoke on the condition of anonymity because the Sabres did not release those numbers in announcing the signing Thursday night.
The 25-year-old Weber was a restricted free agent. The 2006 second-round draft pick has spent most of the past three seasons in Buffalo.
He earned a regular role last year, during which he emerged as one of the team's more dependable, defensive-minded players.
Weber had a goal and six assists, and a team-leading 92 blocked shots in 42 games last season. Overall, he has six goals, 26 assists and 236 penalty minutes in 174 career NHL games.