Rumours had been swirling this offseason regarding Texas' interest in starting pitching.
Moore's best season came in 2013, when he went 17-4 with a 3.29 ERA.
The Giants are not expected to receive big-time prospects in the deal, which is normally the case when the other team is taking on salary.
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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 joins a rotation with two other lefties in 13-game victor Martin Perez and Cole Hamels, who won 11 games this year. Counting Moore, the Rangers have added three options to their rotation. Moore was due to make $9 million in 2018, so this clears a significant amount of money off San Francisco's books for them to bring someone else on board (like Jay Bruce?) for next year.
Moore pitched some tremendous games for the Giants in 2016, including a near-no-hitter at Dodger Stadium and eight innings of two-run ball in Game 4 of the Division Series against the Cubs, which the Giants lost after a ninth-inning bullpen meltdown. He was 6-15 with a 5.52 ERA and 1.53 WHIP. His contract also includes a club option for $10 million in 2019 or a $750,000 buyout. He had surgery in August to fix a torn right flexor tendon.