Sources told Yahoo Sports and The Sports Network that the deal is worth $2.2 million. Monroe, 28, averaged 10.3 points, 6.9 rebounds and 2.2 assists per game in 51 appearances last season for the Milwaukee Bucks, Phoenix Suns and Boston Celtics.
The 6-foot-11, 265-pound Georgetown product was traded from the Bucks to the Suns in November before being waived in February. He signed with the Celtics seven days later. Monroe, the No. 7 overall pick in the 2010 NBA Draft, played his first five seasons for the Detroit Pistons.
He has averaged 13.7 points, 5.7 rebounds, 2.3 assists, and 1.1 steals per game during his eight-year NBA tenure.
Sources told TSN that Monroe is expected to backup Raptors starting center Jonas Valanciunas. The Lithuanian averaged 12.7 points and 6.6 rebounds per game last season for the Eastern Conference regular-season champions.