The deal is worth around $6.6 million, a source close to Franson said.
The team announced the signing Thursday, a week before players report for training camp.
Last year, Franson had a career-best 36 points (seven goals, 29 assists) in 78 games split between Nashville and Toronto.
Overall he has 35 goals and 134 assists in 400 games over six seasons
Franson has an opportunity to be a top-four blueliner in Buffalo. He becomes the latest offseason addition to a Sabres team that is retooling after coming off two consecutive last-place finishes.
Information from The Associated Press was used in this report.