Bibby's agent, David Falk, said Tuesday he has reached an "oral understanding" that will allow the Hawks to retain the point guard who has led the team to two straight playoff appearances.
"We've reached an agreement in principle that hopefully will be announced very soon," Falk said.
Bibby was an unrestricted free agent. Wednesday is the first day NBA free agents are allowed to sign contracts.
Hawks general manager Rick Sund said Tuesday he could not comment on the status of the talks with Bibby.
The Atlanta Journal-Constitution first reported Tuesday that Bibby and the Hawks had a three-year agreement for about $18 million, according to sources.
Falk said the agreement is a good fit for both parties. He said the 31-year-old Bibby has enjoyed his time playing for Atlanta coach Mike Woodson, who has leaned on the 11-year veteran to lead a young team.
"It has been a very good environment for Mike," Falk said. "He enjoys playing for Coach Woodson, who has allowed him to be a coach on the floor."
Bibby made $14.9 million this season.
Falk said Bibby and other free agents have found "the market is extremely conservative this year for free agents, compared to last year."
"A number of teams had interest in him ... but I think Mike was comfortable in the environment" with the Hawks, Falk said.
"He wanted to stay with a team making a commitment to win," Falk said. "He has stabilized the team, given it direction."
The Hawks are re-signing Bibby after drafting another point guard, Jeff Teague of Wake Forest, in the first round last month and trading for guard Jamal Crawford.
Woodson has said the Hawks couldn't have reached the playoffs in 2008 for the first time since 1999 without Bibby.
The Hawks acquired Bibby from Sacramento on Feb. 16, 2008, sending four players and a second-round draft pick to the Kings.
Before the trade for Bibby, point guard was a weak spot for the team. Former general manager Billy Knight passed on point guards Chris Paul and Deron Williams when making Marvin Williams the No. 2 overall pick in 2005. Deron Williams and Paul were the next two picks.
Bibby averaged 14.9 points and 5.0 assists per game last season as the Hawks won 47 games and advanced to the second round of the playoffs.
Marvin Williams is a restricted free agent and may be Sund's next priority. Crawford may fill the role of another restricted free agent, guard Flip Murray, who averaged 12.2 points as the top scorer off the bench.
Another top backup, center Zaza Pachulia, also is a restricted free agent.
Information from The Associated Press contributed to this report.