Financial terms of the deal were not disclosed.
Johnson averaged 7.4 points, 3.2 rebounds and 2.1 assists last season with the Memphis Grizzlies in 52 games after being signed by the team in December.
It will be his second stint with the Raptors, after spending the 2010-11 and 2011-12 seasons with the team. He was originally drafted by the Chicago Bulls in the first round of the 2009 NBA Draft.
Johnson was arrested last month for domestic assault after being accused of hitting and choking his wife at their home.