The Wild also received a second-round pick (No. 37) and a third-round pick (No. 70) in the 2020 NHL Draft. The Predators also received a fourth-round pick (No. 101) in the 2020 draft.
Bonino scored 35 points (18 goals, 17 assists) in 67 games for Nashville this season and one goal in four games in the Predators' four-game loss to the Arizona Coyotes in the best-of-5 Stanley Cup Qualifiers.
"I'm excited," the 32-year-old forward said. "Obviously with every trade you go through, there's bittersweet feelings. I love Nashville, I love the guys there, that's the biggest thing, it's a great group of guys. Every team I've been on, you can say that about, so I'm excited to get to [Minnesota]. I've already had a lot of guys reach out and welcome me and my family. From everything I've heard, it's a great organization from top to bottom, it's run really well and it's a great team that's always a playoff contender. I didn't expect to be doing a press conference this morning when I woke up, but here we are, and I'm just trying to make the best of it."
Bonino, who can become an unrestricted free agent after next season, has scored 282 points (122 goals, 160 assists) in 626 games in 11 NHL seasons with the Anaheim Ducks, Vancouver Canucks, Pittsburgh Penguins and Predators, and has scored 48 points (19 goals, 29 assists) in 98 Stanley Cup Playoff games. He was selected by the Ducks in the sixth round (No. 173) of the 2007 NHL Draft.
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Bonino won the Stanley Cup with the Penguins in 2016 and 2017; he and forwards Carl Hagelin and Phil Kessel formed the "HBK Line" that helped Pittsburgh to its 2016 Cup win.
Wild general manager Bill Guerin was the assistant GM during Bonino's time with the Penguins.
"I have known Nick for a while now. We spent time together in our Pittsburgh days and Nick was a big part of those back-to-back Stanley Cup championships," Guerin told NHL Network. "I like what he brings to the dressing room and I like what he brings on the ice. He's extremely versatile and his hockey sense is real strong and so is his competitiveness. I just like the full package of what Nick brings, and to add some draft picks to it as well will help us in the future."
Bonino said being traded to a team with Guerin is an advantage.
"Having that familiarity made it a little bit easier," Bonino said, "especially after getting off the phone with your former GM (David Poile) saying you've been traded. So it's nice to speak with him and excited to get there in person and get to work.
"I've always been good in the locker room. I think he'll expect me to come in and be the type of guy I always am, try to help everybody be the best player they can be, myself, be good, be great out there, and try to help the team win. That's always my goal, and I think that's kind of what they expect from me."
Kunin can become a restricted free agent on Oct. 9. The 22-year-old forward had NHL career highs in goals (15), assists (16) and points (31) in 63 games with the Wild this season. He scored two goals in Minnesota's four-game loss to Vancouver in the best-of-5 Stanley Cup Qualifiers, his first NHL postseason appearance.
The Predators later Wednesday bought out the final four seasons of forward Kyle Turris' six-year contract.
"[Trading Bonino] is a big hole for us in a lot of areas, but it's also time to make some changes," Nashville general manager David Poile said. "The obvious is we get a younger player, 10 years younger. We get a player that has only been pro a couple of years, he's 22, 23 years of age, he plays in all situations, he plays the center, he plays the wing, he plays what I would call a hard game, he has a lot of energy, a lot of bite to him, power play, penalty killing. I think he is just a good all-around player that is going to get better and better. … It wasn't a reflection on our unhappiness with Nick as much as it was how pleased we are to get a player like Luke and the potential that he has."
Selected by Minnesota with the No. 15 pick in the 2016 NHL Draft, Kunin has scored 52 points (23 goals, 29 assists) in 131 regular-season games.
Guerin said the Wild traded Kunin in part to make room for forward Kirill Kaprizov, who signed a two-year, entry-level contract on July 13 after leading the Kontinental Hockey League with 33 goals.
"As you can see on our team, we have a lot of wingers. Kaprizov is coming in this year," Guerin said. "We're looking for a better year from [Mats Zuccarello] and guys like that. There's opportunity here that we need to start making available to other players, so we just had a ton of wingers that we felt we could move on from one of them. Luke just happened to be that guy."
It was the fifth trade by the Wild this offseason, with deals including goalie Devan Dubnyk (to the San Jose Sharks), forward Eric Staal (to the Buffalo Sabres), and forwards Marcus Johansson and Nick Bjugstad coming to Minnesota.
"I've said I'm not going to make change just to make change, I'm going to do things I think make the team better," Guerin said. "And I think we're better. That's no disrespect to anyone else or anyone that's been here, but I think we're better."
With the No. 37 pick, the Wild selected forward Marat Khusnutdinov from SKA St. Petersburg in Russia's junior league. They traded the other pick acquired from the Predators, No. 70, and the No. 132 pick to the Detroit Red Wings for the No. 65 pick and selected defenseman Daemon Hunt from Moose Jaw of the Western Hockey League.
The Predators selected defenseman Adam Wilsby from Skelleftea of the Swedish Hockey League at No. 101.
NHL.com independent correspondent Jessi Pierce contributed to this report