Camby, 38, played for New York from 1998-2002. He was dealt by the Portland Trail Blazers to the Houston Rockets in March for Jonny Flynn and Hasheem Thabeet.
Yahoo! Sports reported Camby will sign a three-year, $13.2 million with the Rockets, who will then trade him to the Knicks for guard Toney Douglas, forward Josh Harrellson, center Jerome Jordan and second-round draft picks in 2014 and 2015.
The move will provide New York with more frontcourt depth and rebounding power to pair with Tyson Chandler while the Rockets got some solid young players, USA Today said.
Camby averaged 4.9 points and 9.0 rebounds in 59 games last season, 19 of them with the Rockets. He has averaged 9.7 points and 9.9 rebounds in 949 career games.
Douglas averaged 6.2 points in 38 games, Harrellson put in 4.4 points over 37 contests and Jordan averaged 2.0 points through 21 games last season for New York.