Smith's decision clears him to test free agency and be eligible for a 20 percent raise based on his $2.382 million salary from this past season.
The New York Times first reported the story, citing an anonymous source.
Smith could get as much as $12.2 million over four years after opting out. Another option for Smith, the paper says, is re-signing with the Knicks for one year with early Bird rights and earning a salary of at least $5.3 million in 2013-14.
A source told ESPNNewYork.com in May that Smith's father, Earl, is going to make a strong case for his son to stay in New York, but "it's very clear that the money is the biggest factor with him."
Smith was signed in mid-February to a prorated share of the Knicks' $2.5 million mini-midlevel exception with a player option for 2012-13 after playing in China during the lockout.
In April, three league sources with knowledge of his contract situation told ESPNNewYork.com that he would be undermining his value on the free-agent market by signing the $2.5 million option.
Smith averaged 12.5 points per game on 40 percent shooting, 3.9 rebounds and 1.5 steals in the regular season. But Smith struggled in New York's first-round loss to Miami, shooting 11-for-48 in the final three games of the series.
Information from ESPNNewYork.com's Jared Zwerling and Ian Begley was used in this report.