The decision allows Hardaway to return to New York on a four-year, $71 million deal, according to league sources.
The Hawks delivered official notification to the Knicks earlier Saturday, before the 48-hour deadline passed, according to sources. League sources earlier told ESPN there was nearly uniform opinion within Atlanta's front office that the contract was simply too steep when measured against the production and potential of Hardaway.
"Bringing back Tim to his original NBA home is an exciting time for him and this franchise," Knicks general manager Steve Mills said.
Hardaway was drafted by the Knicks in the first round of the 2013 draft.
The Knicks' acquisition of Hardaway to the staggering deal is expected to trigger a renewed willingness to work with the Houston Rockets on trade scenarios to unload Carmelo Anthony, league sources told ESPN.
The Rockets have been persistent in their pursuit of Anthony, who is willing to waive his no-trade clause to join Chris Paul and James Harden in Houston, league sources told ESPN, and the Knicks do not imagine a scenario where Hardaway is sharing the floor with Anthony to start the season.
The Knicks' offer sheet to Hardaway contains a 15 percent trade kicker and a player option in the fourth year, and it also includes an unusual provision requiring the team to pay 50 percent of Hardaway's annual salary by Oct. 1 of every season, according to league sources.
The 6-foot-6 Hardaway had a breakout season in 2016-17 for Atlanta, scoring 14.5 points in 28 minutes per game.
The Knicks signed shooting guard Courtney Lee to a four-year, $48 million deal last summer, but the team has no plans to trade him at this point as the Knicks believe Lee and Hardaway can play well together given the value of shooting in today's NBA, sources confirmed.
With the Hardaway contract in place, the Knicks have very little to offer free agents on the market.
The club renounced its rights to free agents Derrick Rose, Sasha Vujacic and Ron Baker to make room for the contract. They also withdrew a qualifying offer to Baker, who was a restricted free agent. Baker, though, already has agreed to a deal with New York. The terms are unknown.
With their current cap situation, the Knicks can sign Baker with a veteran's minimum exception or with part or all of the $4.3 million room exception.
The room exception, a small amount of cap space and veteran's exceptions are the only tools the Knicks have to offer free agents. The club is looking for a veteran point guard to mentor rookie Frank Ntilikina but has limited resources to find one. Rose and Rajon Rondo are among the free-agent point guards remaining on the market.
The Knicks could also obtain a point guard via trade or could open up more cap space in any trade of Anthony.
ESPN's Ian Begley contributed to this report.