Lee's agent, Mark Bartelstein, told ESPN.com on Thursday that the sides have an agreement in principle on a one-year contract.
"We're on the verge of getting this done," Bartelstein said. "I believe David will sign the contract tomorrow."
The contract is believed to be worth $7 million for the 2009-10 season with incentives that could take it to $8 million if the Knicks reach the playoffs.
Fellow restricted free agent Nate Robinson has also reached terms with the Knicks on a one-year deal, according to a source with knowledge of the talks, that will pay him a higher salary than Robinson's $2.9 million qualifying offer.
Negotiations with Lee and Robinson dragged to the brink of training camp with the Knicks determined not to sign to either player to longer than a one-year deal to preserve maximum salary-cap flexibility for the pursuit of a max-contract free agent in the summer of 2010.
The Knicks did offer more than one year to guard Jason Kidd, who decided to return to the Dallas Mavericks in a three-year deal worth $25 million. New York also pursued Grant Hill and Andre Miller and decided against bidding outright for restricted free agent Ramon Sessions, pulling out of the running before Sessions wound up landing a four-year deal worth $16.4 million from the Minnesota Timberwolves.
Lee's summerlong search for a sign-and-trade to secure a longer contract was also hampered by the Knicks' determination to avoid long-term deals, but the double-double specialist managed to secure a one-year salary well above his $2.6 million qualifying offer without missing camp time.
The deals for both Lee and Robinson, sources said, will include incentive bonuses. And both players will count against the Knicks' salary cap as unrestricted free agents next summer -- when New York launches its long-anticipated pursuit of LeBron James -- until they are re-signed, signed-and-traded, signed by another team or their rights are renounced by the Knicks.
"There's never been a player who signed a deal worth more than the qualifying offer on a one-year deal," Bartelstein told NBA.com. "We're very appreciative of that. They did something that's unprecedented...they could have taken a much harder stance on this. We'll deal with next summer when we get to it.
"This was about the most unique situation you could have in the NBA. It was the perfect storm of what you don't want to have."
Marc Stein is a senior NBA writer for ESPN.com.