The Wild announced the news Friday. Connelly led all AHL defensemen in scoring last season with 52 points on six goals and 46 assists while playing for Rockford and Abbotsford.
It's a two-way deal, meaning Connelly will be paid more if he is playing with the Wild and less if he is with the club's AHL affiliate in Houston. From nearby Bloomington, he played three seasons at Colorado College.
The Wild also signed defenseman Justin Falk this week.
Parise and Suter are scheduled to hold an introductory news conference Monday.