The Knicks gave the Atlanta Hawks 71 million reasons, plus a few more, not to match Tim Hardaway Jr.’s offer sheet, and it worked.

Hardaway officially is a Knick again. He returns to the team that drafted him four years ago, a more well-rounded, much richer player.

The Hawks had until midnight Saturday, but they informed the Knicks in the afternoon that they wouldn’t match the four-year, $71-million offer sheet given to Hardaway.

“Bringing back Tim to his original NBA home is an exciting time for him and this franchise,” general manager Steve Mills said in a statement. “As a versatile wing whose game continues to improve, he will fit right into the core of players that make up a roster emphasizing youth, athleticism, accountability and unselfishness.”

That sounds like the end of the Carmelo Anthony era.

Mills has been working on finding a new home for Anthony. Even though Phil Jackson was removed as team president, that mission hasn’t changed.

The Knicks, who are looking for scenarios that would bring back young players and draft picks, are expected to re-engage in trade talks with the Rockets. Anthony reportedly would waive his no-trade clause to play for the Rockets or Cavaliers.

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After trading for Chris Paul, Houston had Paul George and Anthony on its radar. With George having been dealt to the Thunder, the Rockets are focused on Anthony.

ESPN reported that the Rockets, who locked up James Harden with a four-year, $228- million extension Saturday, are turning their “full attention” to acquiring Anthony. Houston has acquired numerous players with expiring or non-guaranteed contracts to use in trades.

Anthony and his close friend Paul have always wanted to play together, and Harden, Paul and Anthony could make the Rockets a Western Conference contender. The Knicks are in rebuilding mode and would rather get assets and clear cap space than buy out the two years and $54 million left on Anthony’s deal.

Signing Hardaway was their first major move in free agency and the first that Mills has made since he was put in charge of the basketball department.

Hardaway, a restricted free agent, averaged 14.5 points last season for the Hawks. His signing leaves the Knicks with only the $4.3-million room exception and minimum salaries to sign free agents, and they still need a point guard.

They could use the room exception on Derrick Rose or Rajon Rondo, and they also could try to acquire a point guard through a trade.

To make room for Hardaway’s contract, the Knicks waived Marshall Plumlee and renounced their rights to Rose, Sasha Vujacic and Ron Baker. But Baker is re-signing with the Knicks on a two-year deal, and they also could try to re-sign Rose.

In addition to the expensive contract they gave Hardaway, the Knicks added some features to deter the Hawks from matching. The contract includes a 15-percent trade kicker and a fourth-year player option and requires the team to pay 50 percent of Hardaway’s annual salary by Oct. 1 of every season.

Given that they spent that much on a player who has been a backup for most of his four-year career, it’s obvious that the Knicks have big plans for Hardaway and want him to be a part of their young nucleus. Kristaps Porzingis, Willy Hernangomez, Hardaway and first-round pick Frank Ntilikina are 25 or younger.

The Knicks still have veterans Courtney Lee, Lance Thomas, Joakim Noah and Kyle O’Quinn. Because it’s doubtful that anyone would want Noah — whom Jackson signed to a four-year, $72-million contract last summer — Lee and O’Quinn would be the most likely to be traded.

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A league source familiar with the team’s thinking said the Knicks want a mix of young players and veterans to help guide them. Getting an experienced point guard to work with Ntilikina, 18, and Baker, who was an undrafted rookie last season, is critical.

The source said the Knicks would like to hold on to Lee and play him with Hardaway. If they deal Anthony, they will need a small forward. Lee and Hardaway are versatile enough to play shooting guard and small forward.

The 6-6 Hardaway started 30 games last season for the Hawks, 11 of them at small forward. He averaged 18.3 points when he started at small forward and 17.5 points and 3.4 assists overall when he started.

Hardaway struggled defensively with the Knicks but improved on that end of the floor playing for the Hawks and coach Mike Budenholzer, a former Spurs assistant.

The Knicks drafted Hardaway with the 24th pick in 2013. He averaged 10.8 points in two seasons before being traded for the rights to Jerian Grant on draft night 2015. Grant subsequently was dealt for Rose last summer.

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When the deal for Baker becomes official, the Knicks will have 11 players with fully guaranteed contracts, including Anthony. They’ve also begun discussions on a multiyear deal with second-round pick Damyean Dotson. Chasson Randle is under contract, but he has a partial guarantee.