According to Alberto Faccini, the transfer has not yet been formalised but a fee of €7 million has been agreed between the two sides and his client has finalised personal terms with the MLS outfit.
"Thigs have worked out well," the American's representative told Radio Radio. "Michael made this choice and closed the deal with Toronto in just two days.
"There is a very important project there for him at Toronto, who have made an investment that is one of the most expensive in recent years.
"For Michael this was a difficult step to take but the choice was dictated by some market movements. Without waiting for January 31, he chose to follow this path also to help the growth of American soccer."
Faccini explained that Roma had wanted to hold onto the United States international but that the 26-year-old felt he would struggle for game time at the Stadio Olimpico following the signing of Radja Nainggolan from Genoa earlier in the week.
"The arrival of Nainggolan contributed to Bradley's decision," he admitted. "At Roma he never caused any problems and felt like an important player for the team, but things have now changed.
"There were many offers for him, also in Serie A, from clubs like Verona and Bologna. But Micheal chose to return in the States after 10 years in Europe.
"It was a tough decision, but one made with the heart. Roma wanted him to stay but it was his choice to move to Toronto."
Bradley is set to become Toronto's second high-profile signing this month, with the Canadian club set to confirm the signing of Tottenham forward Jermain Defoe for a MLS record fee of €7.3 million on Monday.