The deal is worth $3.3 million, according to multiple media reports.
Franson had five goals and 28 assists in 78 games with Toronto last season. He has 28 goals and 133 points in 322 games NHL games with the Nashville Predators and Maple Leafs. He also has four goals and nine assists in 23 playoff games.
The St. Louis Blues received a one-year arbitration award for forward Vladimir Sobotka.
Terms of the deal will be enforced when Sobotka returns to the NHL. The 27-year-old native of the Czech Republic will play for Avangard Omsk of the KHL this season.
Last season, Sobotka had nine goals, 24 assists and 72 penalty minutes in 61 games with St. Louis.
The Blues agreed to terms on a three-year, entry-level contract with forward Ivan Barbashev, their second-round draft choice.
Barbashev, 18, appeared in 48 games with the Quebec Major Junior Hockey League's Moncton Wildcats last season and finished second on the team with 68 points, including a team-high 43 assists.
The Blues signed forward Jeremy Welsh to a one-year, two-way contact.
Welsh, 26, split last season between the Vancouver Canucks and Utica of the American Hockey League.
The forward posted one goal and six penalty minutes in 19 regular-season games with the Canucks, as well as 15 points (seven goals, eight assists) and 14 penalty minutes in 49 regular-season games with the Utica.
The Montreal Canadiens signed first-round draft pick Nikita Scherbak to a three-year, entry-level contract.
Scherbak, a forward, had 28 goals and 50 assists in 65 regular-season games with the Saskatoon Blades of the WHL last season. Montreal selected the 18-year-old Moscow native with the No. 26 overall pick in the draft.
(Editing by Larry Fine)