"Appreciated my time in Houston," Rivers tweeted Sunday night. "Truly amazing experience. Loved the city and the people. Thank you for having my and family."
"Beyond excited for this. Knicks! NYC! Grateful!" he added in a follow-up tweet.
Rivers, 28, settled into a bench role in Houston, averaging 8.8 points in 23.4 minutes per game last season. He was set to make less than $2.4 million this season with the Rockets but decided to opt out of his contract.
The No. 10 overall pick in the 2010 draft, Rivers never lived up to his billing as a top prospect heading into his freshman year at Duke. But the son of Sixers coach Doc Rivers has turned himself into a capable pick-and-roll ball handler and proved especially useful in Houston as a third option behind James Harden and Russell Westbrook.