Clarkson, 29, arrives after six seasons with New Jersey. The right-wing scored 30 goals in 2011-12 for the Devils, but has never topped 20 in any other season.
The 27-year-old Bozak has spent four seasons with Toronto. Signed as a free agent out of the University of Denver, the centre has recorded 53 goals and 81 assists in 238 NHL games, with 48 penalty minutes.
According to reports, Clarkson was signed to a seven-year deal worth $36.75 million US, and Bozak put under contract for five seasons and $21 million.
The Leafs also reportedly re-signed tough guy Frazer McLaren to a two-year deal. McLaren came to Toronto in January from San Jose and overall racked up 102 penalty minutes in 36 games, with two goals and three assists.
The moves Friday by general manager Dave Nonis follow earlier transactions that have seen the Leafs acquire goaltender Jonathan Bernier from Los Angeles and centre Dave Bolland from Chicago.
Also Friday, the Leafs bought out the contract of forward Mikhail Grabovsky after he cleared waivers, making him a free agent.