Kohl announced the deal Wednesday at the BMO Harris Bradley Center hours before the team was to play its final game of a dismal season. The deal is subject to approval by the NBA and its Board of Governors.
Kohl is a former U.S. senator who has owned the team since 1985. Efforts to find new investors ramped up this year, and made it a priority to find owners or investors who will keep the franchise in Milwaukee.
It appears the Bucks won't be going anywhere after Lasry and Edens committed another $100 million to help build a new arena. Kohl also announced he would also donate $100 million to help fund a new arena.
"Milwaukee fans deserve a winning team," Edens said.
Kohl has spoken for years about the need to upgrade or replace the Bradley Center, the team's downtown home which opened in 1988.
"We should be shouting from the rooftops because this is a game-changer for this entire debate," Milwaukee Mayor Tom Barrett said.
Edens said he hopes to get a plan for a new arena in a year, and have it built in a couple years. He said he thought about $400 million could be a benchmark for building the facility.
With the worst record in the NBA, Milwaukee is in position for a high draft pick.
The Bucks were sold to Kohl for $18 million in 1985. Kohl, 79, is a Milwaukee native whose family owned a chain of department stores.
Lasry is chairman and chief executive officer of Avenue Capital Group, while Edens is co-founder and a chairman of the board at Fortress Investment Group. Both are based in New York.
In Madison, Gov. Scott Walker said he was pleased with the deal that will keep the team in Wisconsin, and that he will work with the new ownership team to see how he can help the team "flourish in the state."
"I think it's a big deal," he told reporters when asked about the sale. Walker said he appreciated Kohl's purchasing of the team and keeping it in Wisconsin. "My hat's off to him and the many years he's committed to the Bucks."
The Bucks were an NBA-worst 15-66 entering Wednesday night's game against the Atlanta Hawks. Milwaukee has already set a franchise record for futility.
The team was beset by injuries from training camp in coach Larry Drew's first season. Center Larry Sanders and guard O.J. Mayo are among the veterans who have been sidelined for long spurts.
Brandon Knight has emerged as a scoring point guard, while 18-year-old Giannis Antetokounmpo had a promising first year after being drafted in the first round last year.