Cobb was 5-15 with a 4.90 ERA in 28 starts for the major-league-worst Orioles in 2018.
The right-hander signed with Baltimore last season after spending six seasons with the Tampa Bay Rays. He got off to a bad start, with a 6.54 ERA at the All-Star break, but found his form in the second half of the season.
"We feel like he's earned it," Hyde said. "His track record speaks for itself, and we're just excited about naming him Opening Day starter."