Clooney founded the Casamigos brand four years ago with partners Rande Gerber and Mike Meldma.
Diageo said it will pay $700 million for Casamigos at first, and then pay another $300 million over 10 years if the brand reaches certain performance milestones.
London-based Diageo's other brands include Johnnie Walker, Guinness and Captain Morgan.
Clooney and Gerber, an entrepreneur who is married to model Cindy Crawford, have appeared in ads for the brand.
Diageo says the founders will continue to promote Casamigos and have a say in its future.
The deal is expected to close in the second half of this year.
Hollywood superstar Clooney wrote in a statement: "If you asked us four years ago if we had a billion dollar company, I don't think we would have said yes.
"This reflects Diageo's belief in our company and our belief in Diageo.
"We'll still be very much a part of Casamigos. Starting with a shot tonight. Maybe two."