ESPN's Jeff Passan reported the deal is worth $33.5 million.
Davis joined the A's in a February 2016 trade after three years with the Milwaukee Brewers and immediately became one of MLB's most dangerous sluggers. He hit 133 home runs over the last three seasons.
He posted a .247/.326/.549 triple-slash line with 48 homers across 151 games in 2018. It marked the fourth straight season he finished with a .247 batting average—an incredible statistical oddity.
"I know he's going to hit .247 next year," A's executive vice president of baseball operations Billy Beane jokingly told reporters in October. "We can count on that consistency. We also know he's going to hit 40 home runs. I'm a big fan of the home run."
The 31-year-old California native signed a one-year, $16.5 million contract with Oakland in January to avoid arbitration and could have become an unrestricted free agent next offseason.
Last April, the former Cal State Fullerton standout expressed interest in remaining with the A's.
"I want to be an Oakland Athletic," Davis told reporters. "I think I fit in well here. I like the organization, I like the coaching staff, I like my teammates."
While Davis is a major threat at the plate, he was mostly restricted to DH work in 2018 because of his past struggles in the field. He posted minus-13 defensive runs saved in 2017, according to FanGraphs.
That said, he'll remain a key cog in the middle of the Oakland order for the foreseeable future.