He was called up by the Astros on July 12, 2013, and made his MLB debut against the Tampa Bay Rays.

Cosart pitched 8+ innings with 2 strikeouts, 2 hits allowed, and 3 walks issued, to get his first major league win.

On July 31, 2014, the Astros traded Cosart, Enrique Hernández, and Austin Wates to the Miami Marlins for Jake Marisnick, Colin Moran, Francis Martes, and a compensatory draft pick.

[10] On July 29, 2016, the Marlins traded Cosart, Josh Naylor, Carter Capps, and Luis Castillo to the San Diego Padres for Andrew Cashner, Colin Rea, Tayron Guerrero, and cash considerations.

[13] His younger brother, Jake Cosart, was drafted by the Boston Red Sox in 2014 and has pitched in Minor League Baseball.