The Knicks had until midnight to equal Houston's three-year $25.1 million proposal for the restricted free agent, but decided the valuation was too steep for their resources.
The 23-year-old Lin exploded onto the NBA scene last season as an undrafted and overlooked Ivy League student, who briefly breathed new life into a stuttering Knicks side and made headlines around the globe for his livewire performances.
Lin's breakout campaign was cut short in March, however, when he suffered a season-ending knee injury and missed the playoffs after averaging 14.6 points and 6.2 assists in 35 games of the lockout-shortened season.
"Much love and thankfulness to the Knicks and New York for your support this past year. Easily the best year of my life," Lin tweeted shortly before the deadline passed.
"Extremely excited and honored to be a Houston Rocket again!"
The Los Angeles-born Asian-American had a brief spell with Houston last December, completing seven minutes in two pre-season games before he was cleared off the payroll and claimed by New York.
Depleted by injuries to key players, Lin made the most of his opportunity to shine in New York with a 25-point game against New Jersey in early February and led the Knicks to seven straight wins, scoring 20 or more in all but one of them.
While his global popularity increased, his on-court performances declined as All-Stars Amar'e Stoudemire and Carmelo Anthony returned to the line-up, and coach Mike D'Antoni, whose pick-and-roll approach favoured Lin's style, resigned.
The Knicks had previously said they would match any offer made for Lin but were blindsided by Houston's back-loaded contract that will pay him $14.8 million in his third year.
The franchise instead opted to take a cheaper route and Lin's place in the roster will be taken by newly acquired point guard Raymond Felton.