Evan Grant of the Dallas Morning News confirmed the deal Sunday, noting it will include an invitation to spring training.
The six-year veteran first baseman played 74 games for the Oakland Athletics last year, batting .229/.301/.350 with three home runs, 20 RBI and 19 runs scored.
If he makes the major league roster, the 28-year-old will have a chance to rejoin Rangers manager Jeff Banister, who was the bench coach of the Pittsburgh Pirates when Davis played there in 2014.
A 2008 first-round pick of the New York Mets, Davis spent his first four-plus seasons in Queens, where he hit a career-high 32 home runs in a career-high 156 games in 2012.
The team sent him to the minors in 2013, and he battled hip and quadriceps injuries through most of the 2014 season. Last year, he underwent season-ending surgery to repair a torn hip labrum in August.
He'll provide the Rangers with another left-handed option at first alongside Prince Fielder and Mitch Moreland. Citing a team source, Grant noted that "Davis will simply give the Rangers more insurance in the event of an injury to Fielder or Moreland."