The Nets are sending center Justin Hamilton, a 2018 lottery-protected first-round pick and a second-round pick to Toronto.
Carroll is owed $30 million over the next two seasons as part of the four-year, $60 million deal he signed upon joining the Raptors two years ago.
Carroll, 30, was a disappointment last season when he averaged 8.9 points and shot 40 percent from the field. Injuries limited him to 26 games in his first season with the Raptors when he averaged 11 points.
Carroll has career averages of 8.1 points and 3.8 rebounds over eight NBA seasons. The Nets will be the seventh NBA team to employ him.
Hamilton averaged 6.9 points and 4.1 rebounds last season. He has career marks of 6.1 points and 3.6 rebounds in 113 NBA games.