Mrs Sterling said in a statement: "I am delighted that we are selling the team to Steve, who will be a terrific owner. We have worked for 33 years to build the Clippers into a premiere NBA franchise. I am confident that Steve will take the team to new levels of success."
Ballmer added: "I love basketball. And I intend to do everything in my power to ensure that the Clippers continue to win, and win big, in Los Angeles.
"LA is one of the world's great cities, a city that embraces inclusiveness, in exactly the same way that the NBA and I embrace inclusiveness. I am confident that the Clippers will in the coming years become an even bigger part of the community."
The NBA will have the final say on the sale, but ESPN reports that the agreement has already been sent to the league for approval.