Former U.S. senator Herb Kohl reached agreement with them last month for a price tag of about $550 million after they pledged to keep the team in Milwaukee. The NBA said Thursday in a statement that the transaction is expected to close shortly.
The league's expected approval comes days before the NBA holds its draft lottery. The Bucks, who had a league-worst 15 wins, have the best odds to get the No. 1 pick next week for June's talent-rich draft.
"The Bucks and their fans will benefit greatly from their vast business experience, energy and strong commitment to Milwaukee," commissioner Adam Silver said in a statement.
Lasry and Edens committed to providing $100 million to help build a new arena. Kohl also announced he would donate $100 million for a new facility to replace the BMO Harris Bradley Center, the team's downtown home, which opened in 1988.
Edens had said he hoped to get a plan completed for a new arena in a year, and have it built in a couple of years. He thought it might take about $400 million to build a new facility, though the new owners might face a tricky task in seeking public funding if they don't get more private help.
Kohl bought the Bucks for $18 million in 1985. The Milwaukee native, whose family owned a chain of department stores, was hailed as a hometown hero.
Silver praised Kohl for his "unprecedented and historic financial gift toward the construction of a new Milwaukee arena and for his outstanding service to the league and his community over his nearly 30-year tenure."
An injury-plagued season left the Bucks a franchise-worst 15-67. They have finished above .500 only three times since 2000, though Milwaukee did make the playoffs in 2012-13. The Bucks were swept in four games by Miami in the first round.
With new owners and a 25 percent chance to pick up the No. 1 pick in the draft, the Bucks face a defining offseason. Even if it doesn't win the lottery, Milwaukee cannot fall below the fourth pick in a draft stocked with top prospects, including Duke's Jabari Parker and Kansas' Andrew Wiggins.