According to Jon Heyman of FanRag Sports, the two sides agreed on a $10.5 million deal.
Davis has spent the past two years in Oakland after starting his career with the Milwaukee Brewers. In that time, he has become one of the top power hitters in the game, hitting 42 home runs in 2016 and 43 in 2017.
As the team noted, his 85 home runs in the last two years trail only Giancarlo Stanton (86) for the most in the majors.
The 30-year-old also earned MVP votes for the first time last season after leading the team in home runs, RBI (110) and slugging percentage (.528). His .864 OPS was also the highest for any full season of his career.
Davis has one more year under arbitration before potentially becoming a free agent following the 2019 season.
The Athletics have done a good job in avoiding long-term contracts during their current rebuild. According to Baseball Reference, the only contracts that last longer than the upcoming season are Stephen Piscotty and Yusmeiro Petit, both of whom were acquired this winter.
However, the organization might have to fork up the cash for Davis, who has been the team's most feared hitter over the last two years.
If he keeps up his power numbers over the next two years, he could have a lot of suitors on the open market.