Stoudemire agreed to the move earlier this week, but under NBA free-agency rules it couldn't be announced until Thursday.
Stoudemire is a five-time all-star who had played his entire eight-year NBA career with the Phoenix Suns before opting out of his agreement with Phoenix after this season. The Suns were to have paid him $17.7 million next season.
The 6-foot-10 forward-center averaged 23.1 points and 8.9 rebounds over 82 games with the Suns in 2009-10. Stoudemire was the NBA rookie of the year in 2003 and has averaged 21.4 points and 8.9 rebounds a game over his career.
"Amare is one of the most talented players I have ever worked with and I'm excited to welcome him to New York," said Knicks Coach Mike D'Antoni, who coached Stoudemire for five seasons in Phoenix. "He has thrived in our system and will be a great addition to our team."