The deal is for $750,000 with incentives in 2019, with a $3-million team option that follows in 2020, Mark Gonzales of the Tribune reported.
Barnette, 35, had a 2.39 ERA and 0.91 WHIP in 22 appearances for the Rangers in 2018. He has a career 3.50 ERA in 144 innings across three MLB seasons. He had a 5.2 strikeout-to-walk ratio in 2018 and a 3.07 mark for his career.
In another roster transaction, left-hander Ian Clarkin cleared waivers and has been assigned to Triple-A Iowa.