Atlanta claimed Grove off waivers from Tampa Bay on Tuesday and optioned him to Triple-A Gwinnett.
Grove was designated for assignment by the Rays over the weekend after spending the past month in the minors. The right-hander made three appearances for Tampa Bay this year, giving up four earned runs with a 6:0 K:BB across seven innings. He was more effective at Triple-A Durham with a 3.55 ERA, 1.33 WHIP and 39:14 K:BB over 33 innings.