The contract carries an average annual value of $3.325 million, according to ESPN's Pierre LeBrun.
Sportsnet's Chris Johnston has a more specific breakdown of the deal:
The two sides worked on the contract in Buffalo on Wednesday night.
The 28-year-old struggled offensively upon his return to Nashville, registering four points in 23 regular-season contests and two points in five playoff games.
Franson was a third-round pick of the Predators in 2005.