Zidlicky, 31, spent four seasons with Nashville and had 175 points and 299 penalty minutes in 307 games. Last season, he led Predators defensemen in points and assists. He will help fill holes left by Kurtis Foster's injury and the departures of Keith Carney and Petteri Nummelin.
Jones was Minnesota's fourth-round pick in the 2004 draft. Last season, he played in eight games for AHL Houston after leaving Miami of Ohio.
By bringing back Brunette, the Wild are adding a player who is popular among teammates and fans. He played three seasons in Minnesota from 2001-04 and ranks third on the franchise career list in assists, fifth in points and seventh in goals.
He will give the team a durable presence in front of the goaltender and an opportunistic scorer. Wild general manager Doug Risebrough has said on several occasions that he should not have allowed Brunette to leave for Colorado in 2004.
"Andrew is a consistent offensive performer and an excellent teammate who helped create the culture of our team," Risebrough said in a statement. "We are better, on the ice and in the dressing room, with him back. Not often do you get the chance to correct a mistake."
The 34-year-old Brunette had 19 goals and 40 assists last season with the Avalanche and has played in 453 consecutive games, the longest active streak in the NHL.