The deal is worth $9.5 million, with a salary-cap hit of $4.75 million, NHL.com reported.
Connolly agreed to terms Saturday following a strong season with the Buffalo Sabres in which he had 13 goals and 42 points in 68 games. He will be entering his 11th NHL season, having also spent time with the New York Islanders. In 627 career games, Connolly has 118 goals and 277 assists.
Connolly has five goals and 18 assists in 36 career playoff games. He had two assists in Buffalo's first-round loss to the Philadelphia Flyers last season.
Information from The Associated Press was used in this report.