Leonsis, a former AOL executive, and the Pollins ran into some snags in talks this year, but in a statement Tuesday, Pollin's sons, Robert and James, said they and their mother, Irene, congratulate Leonsis on this "near-final step in a long negotiation."
A person familiar with the negotiations confirmed to The Associated Press last month that the two sides agreed to value the franchise and the arena at slightly more than $550 million.
Pollin died at age 85 in November, setting in motion what was expected to be a smooth transfer of the Wizards and the Verizon Center to Leonsis.
Pollin anointed Leonsis as his heir when the two became partners in 1999. Leonsis' group already owns 44 percent of the team and the arena and was given the right to get the first chance to purchase the remaining 56 percent.
"It's not a 'done, done' deal, but it's fairly close," Robert Pollin said in a telephone interview Tuesday. "A signed deal should be a matter of days."
The NBA Board of Governors will need to approve the sale, but Robert Pollin said, "There's really no question that they will. They know Ted. ... It's a foregone conclusion they will approve it."
A representative for Leonsis' group had no comment Tuesday.
Abe Pollin was the NBA's longest-tenured owner, having bought the Baltimore Bullets in 1964. He renamed his NBA team in 1997 because of the violent connotation of the word "Bullets." A builder by trade, Pollin constructed the Verizon Center, which helped revitalize Washington's downtown area.
Pollin previously sold Leonsis the NHL's Capitals in 1999, and the WNBA's Mystics in 2005.
"Obviously, very sad feelings about transitioning out of it, but compared to losing my father, it's not the same category," Robert Pollin said. "It was his project for most of his adult life. I was 13 when we bought the Bullets."
The Wizards are coming off consecutive last-place finishes, including a 26-56 record in 2009-10, a season marred by the suspension of star Gilbert Arenas for bringing guns into the locker room.