Per John Shea of the San Francisco Chronicle, the Giants will receive prospects from the Rangers in exchange for the left-hander. Alex Pavlovic of NBC Sports Bay Area reported San Francisco will receive two minor-league pitchers and cash.
Shea previously reported the Giants were nearing a deal involving at least one of Moore and Hunter Pence in an effort to shed salary.
The Giants have been linked to multiple high-profile free agents and trade targets this offseason, though they have yet to make any additions to their roster.
USA Today's Bob Nightengale reported the Giants were expected to intensify their pursuit of Jay Bruce after the Stanton deal fell apart.
Since being acquired by the Giants in July 2016, Moore has posted a 5.12 ERA with 217 strikeouts in 242.2 innings over 44 appearances. He's owed $9 million next season with a $10 million team option for 2019.
The Rangers are in need of depth in their starting rotation, which Moore will help fill. Their starters ranked 17th in MLB with a 4.66 ERA last season, despite having Yu Darvish through July and Cole Hamels.
Adding Moore to the mix gives Texas a group of starting pitchers for 2018 that includes Hamels, Martin Perez, Doug Fister and Mike Minor.