The Rangers non-tendered Webb on Friday.
Webb signed a one-year deal with the Rangers in December after spending the 2024 campaign with the Orioles, but the 32-year-old right-hander will now be on the lookout for a team in need of bullpen depth. He finished the 2025 regular season with seven holds along with a 3.00 ERA, 1.03 WHIP and 58:19 K:BB across 66 innings.