Toronto sent a first and second-round pick in the 2010 draft to Boston, along with another first-round pick in 2011.
Kessel scored 36 goals and added 24 assists in 70 games with Boston last season.
"Bringing Phil Kessel aboard, it's a statement to our players that we intend to be competitive right away, and I think he gives us a dimension that we need," Maple Leafs general manager Brian Burke said.
"(Kessel) told me he's walking on air. This is a free agent that could have signed with other teams, he wanted to sign with us, and I think it's an important pick up for us."
The 21-year-old forward, who's entry-level deal expired after last season, failed to negotiate a contract extension with Boston in the offseason.
The Bruins picked Kessel fifth overall in the 2006 draft. Kessel had shoulder surgery over the summer and won't be ready to play until at least November.
The trade represents a possible change in strategy for Burke. Up until now, he's been content to stock up on draft picks and defenseman, but has done little to bolster the Leafs' offense.
While giving up three high draft picks is a big price for Kessel's negotiating rights, the Leafs also have several promising rookies in Tyler Bozak, Viktor Stalberg, Nazem Kadri and Christian Hanson, all of whom have scored in the team's first two preseason games.
"It's a very high price but it's one we feel makes sense for us and I think what's made it possible to expend those picks is two focuses: one is that he's a young player, he's not even 22 yet," Burke said.
Burke, who nearly had a deal in place with Boston for Kessel at the draft, didn't give up his pursuit of the talented forward. His job was made easier last week when Kessel broke off talks with the Bruins.
"It's taken a long time, it's taken a lot of effort, but I think it's worth it," Burke said.