The deal will pay him $2.5 million next season, $3 million in 2013-14 and $3.75 million in 2014-15.
Foligno was acquired from the Ottawa Senators on Sunday.
The Jackets gave up one of their top defensemen in Marc Methot for the restricted free agent.
Foligno, a native of Buffalo, N.Y., has 61 goals and 87 assists with 299 penalty minutes in 351 career games, all with the Senators.
He was the Senators' top draft pick in 2006. He had a career-high 17 goals in 2008-09 and has at least 14 goals and 32 points in his four full NHL seasons. He also has played in 177 consecutive games.
Information from The Associated Press was used in this report.