Arn Tellem, Johnson's agent, said that Johnson was impressed with the team's commitment to him and agreed to accept the club's six-year contract offer. He confirmed the post to The Associated Press.
Atlanta offered Johnson, a four-time All-Star, approximately $119 million over six years -- nearly $27 million more than any other team could offer.
The Hawks would not comment, citing the NBA's moratorium on signings. Deals can't become official until Thursday.
"When the free agency period kicked in, Joe made a point of talking to the Hawks first," Tellem wrote in the blog post. "Their owners and new coach, Larry Drew, impressed Joe with their commitment to making the team championship-caliber. In turn, Joe felt equally committed to the Hawks, his teammates and the city of Atlanta."
Tellem said Johnson, who was wooed by a number of other teams, could have forced a sign-and-trade to another team, but "decided that winning in Atlanta would be more meaningful."
Free-agent center Shaquille O'Neal is also drawing interest from the Hawks, league sources told ESPN The Magazine's Chris Broussard.
An AOL Fanhouse report on Monday said O'Neal has been offered a two-year deal starting at the mid-level exception by Atlanta and that O'Neal is seriously considering it.
"I think he wants to see how everything shakes out with all the free agents, but he's seriously considering Atlanta's offer," a source told AOL Fanhouse. "He wants to play two more years, and he wants it to be with a contender. He thinks he can help them become a serious one."
However, his agent, Perry Rogers, denied that an offer had been made.
"We have had no offers from the Hawks,'' Rogers told ESPN.
According to AOL Fanhouse, Johnson was told by management that the Hawks intended to make significant changes to their roster, including the possible addition of O'Neal.
The New York Knicks were the first team to meet with Johnson when he became a free agent at 12:01 a.m. ET Thursday, making it known that he was among the players atop their wish list. The Chicago Bulls contacted Johnson as well, but did not meet with him.
But Johnson did not agree to the Hawks' offer immediately, and as of Friday, sources said Johnson was still considering offers from the Knicks and Bulls.
Teams were courting Johnson with the hope that he could be the first domino in luring one of the top-tier free agents in LeBron James or Dwyane Wade. The Knicks made Johnson their first priority with the hope that if they didn't land James, he could reunite in New York with former Phoenix Suns coach Mike D'Antoni and ex-Suns teammate Amare Stoudemire.
"For his next act, Joe plans to actively recruit other top free agents to Atlanta, a place not unlike his hometown, where he feels comfortable and appreciated," Tellem wrote. "LeBron, you've already met with the front offices of six teams. How about considering the Hawks?"
Johnson has been at the center of the Hawks' resurgence since arriving in Atlanta from Phoenix in a sign-and-trade deal on Aug. 19, 2005. A 13-win team the season before he arrived, the Hawks doubled that the next season and went 53-29 in 2009-10 before getting swept by Orlando in the Eastern Conference semifinals.
Johnson averaged 21.3 points during the regular season but played poorly during that series, creating speculation he may have cost himself max dollars. And there was thought he may want out of Atlanta, anyway, since he turned down a $60 million extension last summer and was critical of the team's fans this season.
Information from ESPN.com senior NBA writer Chris Sheridan and The Associated Press was used in this report.