The 38-year-old Camby agreed Monday to rejoin the Knicks in a deal that sends three players and two second-round draft picks to Houston, according to a person with direct knowledge of the move.
The person spoke on condition of anonymity because neither team has announced the trade.
Yahoo Sports reported that Camby's deal was for three years and $13.2 million.
The Rockets will get guard Toney Douglas, centres Josh Harrelson and Jerome Jordan and second-round picks in 2014 and '15.
The 6-foot-11 Camby, meanwhile, will be back in New York where he played from 1998-2002.
Douglas played in 38 games last season, starting only nine, and averaged 6.2 points and 2.0 assists. The 6-10, 275-pound Harrelson was a second-round pick by New Orleans in 2011 and was traded to the Knicks. He appeared in 37 games and averaged 4.4 points and 3.9 rebounds. The 7-foot Jordan, a native of Jamaica, averaged 5 minutes in 21 games last season.
Though Camby has battled injuries during his NBA career, he remains a productive rebounder and shot blocker even after 16 seasons. He also drew interest from Miami and New Jersey but made his destination clear on Twitter, with a simple posting of "NY" on Monday afternoon.
Camby helped the Knicks make a surprising run to the 1999 NBA Finals in his first season in New York. The No. 2 overall pick in the 1996 draft and a native of nearby Connecticut became a fan favourite before the Knicks dealt him Denver in 2002. He should become a valuable backup at centre to Tyson Chandler, last season's NBA Defensive Player of the Year.
He becomes the second nearly 40-something to join the Knicks this summer, with Jason Kidd agreeing to go to New York last week. The deals cannot become official until Wednesday.
The Knicks had announced earlier Monday that all three players going to Houston would headline their summer league roster.
Douglas was the Knicks' starter at point guard to begin the season but struggled coming off off-season shoulder surgery. He quickly lost his starting job and eventually fell out of the rotation completely, even after injuries to Jeremy Lin and Baron Davis.
The Knicks and Rockets are also competing for Lin's services. Houston, one of the most active teams in the off-season, got Lin to agree to a four-year deal, but he is a restricted free agent, and the Knicks have three days after Wednesday to match the Rockets' offer.
The pursuit of Lin emerged after unrestricted free agent point guard Goran Dragic went to Phoenix. The Rockets immediately reached out to Lin and traded Kyle Lowry to Toronto.
Houston obtained Camby from Portland at the trading deadline. He averaged 7.1 points and 9.3 rebounds in 19 games. The Rockets traded starting centre Samuel Dalembert before last month's draft, among the flurry of moves by general manager Daryl Morey after the team missed the playoffs for the third straight season.
The Rockets collected three first-round picks before the draft and were rumoured to be building a package to offer Orlando for All-Star centre Dwight Howard. But Houston couldn't pull off a draft-night deal, and the Rockets drafted guard Jeremy Lamb and forwards Royce White and Terrence Jones.
Houston continued to manoeuvr after the draft, getting Bulls centre Omer Asik to agree to a three-year, $25 million deal. The 7-foot Asik is a restricted free agent, giving Chicago three days to match Houston's offer.
Houston withdrew its qualifying offer to guard Courtney Lee, allowing him to become an unrestricted free agent.
AP Basketball Writer Brian Mahoney contributed.