The Penguins sent forward prospect Kasperi Kapanen, forward Nick Spaling, defenseman Scott Harrington and a 2016 third-round pick to the Maple Leafs for Kessel, forward Tyler Briggs and defenseman Tim Erixon. Conditional draft picks are also involved.
In addition, Toronto will retain 15 percent of Kessel's salary, or $1.2 million annually, a source said.
The teams announced the deal Wednesday, hours after the start of NHL free agency.
Penguins general manager Jim Rutherford made no secret about his wish to go big-game hunting in the hopes of landing a top-six winger. Though he was unsuccessful in doing that during last weekend's draft, his patience ultimately paid off as he was able to land Kessel on the first day of free agency.
The 27-year-old Kessel collected 25 goals and 36 assists this past season for the Leafs, his sixth with the team. He has 247 goals and 273 assists in nine seasons between Boston and Toronto.
He was rumored to be on the move for some time now, especially with the Leafs in rebuilding mode and the team looking to complete an overhaul in the wake of another abysmal season. They finished 30-44-8, leading to them hiring Mike Babcock as coach.
"(Kessel) was always the guy, he was a guy that was blamed when things weren't going well, and he doesn't have to be the guy here," Rutherford said. "We have a bunch of them, and so I believe that he's going to fit in very well."
Team president Brendan Shanahan said before the draft that the Leafs would not make any move hastily when it came to Kessel, though he characterized the interest in the five-time 30-goal scorer as strong.
"I think it's a good fit for Phil," Shanahan said. "At the same time it stays on our message -- with what we were doing here as a group wasn't working."
"We are happy to have him, he has a ton of speed and a great scoring touch. He will help our team a lot," Crosby said of Kessel in an email to ESPN.com's Pierre LeBrun.
Pittsburgh believes forward Pascal Dupuis will be back in 2015-16 after missing most of last season with blood clots in his lungs. While Dupuis has proven effective when teamed with Crosby, Kessel's arrival gives Crosby a proven finisher. Kessel is also one of the more durable players in the league. He hasn't missed a game in five seasons.
Kessel has five years remaining on a deal that carries a cap hit of $8 million annually. Though the Pens likely will face some cap issues in the future, Rutherford was able to pull off the deal without sending back either of the team's top two young defenseman, Olli Maatta and Derrick Pouliot.
"I believe we improved our team," Rutherford said. "It's hard to score goals in this league. We play a lot of one-goal games and when you can get a pure goal scorer, that's going to give you a better chance to win games."
Kapanen, taken with the 22nd overall pick in the 2014 draft, was considered one of the top forward prospects in the Penguins' organization.
The Penguins also signed Russian forward Sergei Plotnikov on Wednesday. The 25-year-old forward agreed to a one-year deal. Plotnikov had 15 goals and 21 assists for Lokomotiv Yaroslavl of the KHL last season.
"We have to get him over here and see him, actually see him in our group but he's a real good player," Rutherford said. "Whether he can play in our top six or not, we'll find out."
Information from The Associated Press was used in this report.