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."