The United States international becomes the MLS outfit's third designated player signing following the captures of Jermain Defoe and Gilberto.
Bradley's switch ends an 18-month spell with Roma and sees the 26-year-old return to the MLS after an eight-year absence.
And the former Heerenveen and Borussia Monchengladbach player is looking forward to representing the Canadian franchise.
"I have never been more excited, more determined or more motivated for any challenge in my entire career," he said.
"(I want) to be a part of this project and this city, to help bring a winning team."
Head coach Ryan Nelsen expressed delight with the players Toronto have been able to attract, despite finishing a lowly ninth in the Eastern Conference in 2013 season.
"I told the players every day that we should always strive to perfection," Nelsen said.
"If I had the chance to pick three designated players, I think we would be getting pretty close to perfection with the players we've brought in."
