Manager Kevin Cash made the announcement Wednesday. Cobb was 10-9 with 2.87 ERA in 27 starts last season and ascended to the top of Tampa Bay's rotation when David Price was traded last summer.
Price was the opening day starter three of the past four years.
Cobb will take the ball at home against Baltimore on April 6. Right-hander Chris Archer and lefty Drew Smyly will follow him in the series against the Orioles, while right-hander Jake Odorizzi will start Tampa Bay's road opener at Miami on April 10.
With Matt Moore still recovering from elbow surgery, the final spot in the rotation will be filled during spring training.