The Mariners designated right-hander A.J. Schugel for assignment to make room on their 40-man roster.
Wieland, a fourth-round Draft pick by the Rangers in 2008, has a 45-27 record and 3.52 ERA in his Minor League career, but missed half the 2012 season and all of 2013 due to Tommy John surgery.
Wieland was acquired by the Dodgers as part of the Matt Kemp trade with the Padres last offseason.
Mejia, 21, spent most of last season with Class A Short-Season Everett, though he also appeared in a handful of games for Class A Clinton, Triple-A Tacoma and the Arizona Rookie League.