The sale will be financed by cash and assumption of some debt, sources said.
Hawks CEO Steve Koonin and coach Mike Budenholzer will be part of the long-term plans of the new ownership group, sources close to the process told ESPN's Ramona Shelburne.
In his press conference prior to Game 2 of the Hawks' first-round series against the Brooklyn Nets, Budenholzer said he was aware of the reports of the sale, but was focused on basketball.
"I think everyone is very, very respectful that today we have Game 2 of the first round and that our focus is on the game," Budenholzer said. "I'm fully aware of a lot of things that are going on around us, but there's nothing I have to do besides prepare for tonight and make sure our team is prepared and focused."
The deal, which is expected to be announced later Wednesday, also includes operating control of Philips Arena, sources told Shelburne.
Ressler, an owner of the private equity and investment firm Ares and a real estate developer, was one of three finalists in the Los Angeles Clippers' sale last spring. The group's bid of $1.2 billion fell short of the $2 billion purchase price submitted by Steve Ballmer.
The purchasing group led by Ressler also includes former NBA All-Star Grant Hill, Clayton Dubilier & Rice partner Rick Schnall, Spanx owner Sara Blakely and her husband, entrepreneur Jesse Itzler.
The Hawks went on the market in January following the publication in September of an email written by principal owner Bruce Levenson in 2012 that expressed concern that large numbers of African-American spectators at his team's games were driving away more affluent, middle-aged, white suburban fans.
"My theory is that the black crowd scared away the whites and there are simply not enough affluent black fans to build a significant season ticket base," Levenson wrote.
Levenson was effectively forced into exile, along with general manager Danny Ferry, whose racially insensitive comments on a conference call were also made public.
Yahoo! Sports earlier reported that a deal between the Hawks and Ressler's group was close.
The Hawks, the No. 1 seed in the Eastern Conference, host the Brooklyn Nets in Game 2 of their first-round series Wednesday night. Atlanta leads the series 1-0.
Bruce Levenson selling Hawks for $850M
Kevin Arnovitz reports the latest on Bruce Levenson selling the Atlanta Hawks to entrepreneur Anthony Ressler for $850 million.