Pittsburgh receives forward Alex Galchenyuk and defenseman prospect Pierre-Olivier Joseph in the trade. Arizona also got a fourth-round pick in the 2021 NHL Draft and minor league defenseman Dane Birks.
Kessel had 82 points (27 goals, 55 assists) in 82 games this season and two points (one goal, one assist) in four Stanley Cup Playoff games.
"I'm very excited to be part of the Coyotes," the forward said. "Me and Rick [Tocchet] have a good relationship, excited he's going to be my coach, looking forward to doing great things in Phoenix. ... I'm just coming in to do what I do best, try to help the team win as many games as possible. I think they're a good up-and-coming team. They've got a lot of great pieces in place, lot of good players."
[RELATED: Kessel, Tocchet reunite with Coyotes after trade from Penguins | 2019-20 NHL Trade Tracker]
Kessel, who turns 32 on Oct. 2, was acquired by the Penguins in a trade from the Toronto Maple Leafs on July 1, 2015. In four seasons, his 303 points (110 goals, 193 assists) were second on Pittsburgh behind Sidney Crosby's 363.
In the 2016 playoffs, Kessel had a Penguins-high 22 points (10 goals, 12 assists) in 24 games to help them win the Stanley Cup. He had 23 points (eight goals, 15 assists) in 25 postseason games to help Pittsburgh repeat as Cup champion in 2017.
"I have a lot of good memories. Two Cups, fans treating me great there, the city's great," Kessel said. "Those couple of years there, those will last forever. I'm glad to have a couple of Cups, but it's time to move on."
Video: PIT@DET: Kessel shovels home Crosby's perfect feed
Kessel will be reunited with Tocchet, who was an assistant with the Penguins for three seasons from 2014-17, including when they won the Cup in 2016 and 2017 under coach Mike Sullivan.
"Toch knows him extremely well and coached him and he knows exactly what he's getting with Phil, and Phil knows exactly what he's getting with Toch," Coyotes general manager John Chayka said. "All this gives us comfort we're not only getting a Stanley Cup winner and an elite scorer, but a guy who should fit in well and come in motivated."
Selected by the Boston Bruins with the No. 5 pick of the 2006 NHL Draft, Kessel has 823 points (357 goals, 466 assists) in 996 games with the Bruins, Maple Leafs and Penguins. He has scored at least 30 goals in six of 12 full NHL seasons, most recently when he had 34 in 2017-18.
"We felt we needed a lead horse up front, a guy who's produced offensively consistently," Chayka said. "We were looking for a veteran player who has a history of doing it. We have a lot of players who have a lot of upside and potential, but we needed a player who could be a 20- or hopefully 30-goal scorer. He's been one of best offensive producers in the League for a sustained period of time.
"... We think he augments our [forwards] and leads the way and take us to the next level," Chayka said. "I think it's going to have kind of a cascade effect on our entire lineup, add a lot of synergy to our group so we can take this thing to the next level."
Kessel has three seasons remaining on an eight-year contract ($8 million average annual value) he signed with the Maple Leafs on Oct. 1, 2013.
Penguins general manager Jim Rutherford said they wanted to become "harder to play against" and get "more depth at forward where once you put all the forwards in place, guys can move up and down the lineup."
"I felt it was time to make a change," he said. "We were making some changes, so I kind of made that decision. I'd had times where I'd talked to Phil about the future here and things like that. I was aware that Arizona and going to be with [Tocchet] was a place he'd be comfortable with. We like Alex. We know he can score when he's on the top of his game. He'd already done it. He's had a 30-goal season."
Galchenyuk had 41 points (19 goals, 22 assists) in 72 games this season, his first with the Coyotes. The 25-year-old was acquired in a trade from the Montreal Canadiens on June 15, 2018, for forward Max Domi.
Galchenyuk was selected by Montreal with the No. 3 pick of the 2012 NHL Draft, which was held in Pittsburgh. He has 296 points (127 goals, 169 assists) in 490 NHL games with the Coyotes and Canadiens, and 13 points (four goals, nine assists) in 28 playoff games, all with Montreal.
"That was definitely so special, being drafted there," Galchenyuk said Sunday. "Seven years later, I'm a Pittsburgh Penguin. It's surreal. You can't really explain all of the emotions that I had. I remember it being a great sports city that's one of the best in the country and how great the fans are, even from the draft experience. I remember how passionate the fans are.
"Timing is everything. I feel this is the right time to come to Pittsburgh. Just looking forward to coming to Pittsburgh, to a winning culture. Just enjoy my time there and work hard to help the team to get to the ultimate goal, which is the Stanley Cup."
Video: EDM@ARI: Galchenyuk beats Koskinen short side for PPG
He has one season remaining on a three-year contract he signed with the Canadiens on July 5, 2017. Financial terms were not disclosed.
Rutherford said the trade might allow the Penguins to be active when the free agency signing period begins at noon ET on July 1.
"We're kind of getting a late start on it here because we didn't think we'd be in on it," he said. "But now that we've made this deal, we have a chance to do it. … It opens up flexibility for us at the end of this season. Whether we re-sign Alex or we just use the cap space, we wouldn't have been able to do that if we'd kept Phil. So there were a lot of factors that went into it."
Joseph, who turns 20 on July 1, was selected by the Coyotes in the first round (No. 23) of the 2017 NHL Draft. He has not played an NHL game.
Kessel has played 774 consecutive games, the third-longest active streak in the NHL behind unrestricted free agent forward Patrick Marleau (788) and Keith Yandle of the Florida Panthers (797).
"I've had some injuries but some luck involved there," Kessel said.
Birks was selected by the Penguins in the sixth round (No. 164) of the 2013 NHL Draft. The 23-year-old played 65 games with Wheeling of the ECHL and one game with Wilkes-Barre/Scranton of the American Hockey League this season.
NHL.com staff writer Mike Zeisberger and correspondent Alan Robinson contributed to this report