MacArthur's deal is valued at a total of $6.5 million. Bozak will earn $3 million over the two seasons of his contract.
MacArthur broke out last season with 21 goals and 62 points for the Maple Leafs, nearly doubling his best regular-season point total.
The Thrashers turned down a $2.4-million ruling for MacArthur at the end of last season, which led to Toronto signing him as an unrestricted free agent.
During his five years in the NHL, the Lloydminster, Alberta native has spent time with the Buffalo Sabres and Atlanta Thrashers, accumulating 65 goals and 85 assists, while appearing in 290 career games.
MacArthur was originally drafted by the Sabres in the third round of the 2003 NHL Entry Draft.
Bozak tweeted news of his signing to his supporters on Tuesday, saying "Thanks for the congrats everyone. Glad to be back with the Leafs to play in front of the best fans in the world."
He netted 15 goals and 32 points last year in Toronto. The 25-year-old Regina native played all 82 games in his first full NHL season.
He was originally signed as a free agent out of the University of Denver in April 2009.