Zuccarello gets a five-year, $30 million deal, while Hartman gets $3.8 million over two years.
"It's a really good mixture of players, and I think hopefully with the pieces we got this summer we can be a contender," Zuccarello said.
In his first game with the Stars, Zuccarello had a goal and assist but also broke his arm, putting him on the shelf for a month. He returned to a playoff team. He had four goals and seven assists in the postseason as the Stars were eliminated in seven games by the St. Louis Blues in the conference semifinals.
The 31-year-old completed a four-year, $18 million contract by finishing 2018-19 with 12 goals and 28 assists.
His best season came in 2015-16, when he had career highs in goals (26) and points (61). He posted 59 points the next season and 53 last year.
"The way that this guy competes is going to be contagious for our team," Wild general manager Paul Fenton said, adding: "I would like our team to play with a little more hardness and passion and excitement, and I think he'll not only do it himself, but he'll bring people along with him."
Hartman had 12 goals and 14 assists while playing 83 regular-season games last season. He played 64 games for the Nashville Predators, before getting traded to the Flyers, with whom he played 19 more.
The 24-year-old Hartman has 42 goals and 47 assists in 245 career games over five seasons with the Chicago Blackhawks, Nashville and Philadelphia. He was the 30th overall pick when Chicago drafted him in the first round in 2013.
Information from The Associated Press was used in this report.