The fifth-year senior graduated in December and will be eligible for the 2014 season.
In a statement, Joeckel said he appreciates the support he received while at Texas A&M.
"I have loved my four and a half years at Texas A&M," Joeckel said. "I am glad I had the opportunity to play for Coach (Kevin) Sumlin, Coach (Jake) Spavital and the rest of the coaches. I am proud to have my degree from the Mays Business School and I'll always consider myself a member of the Aggie family."
Joeckel, brother of former Texas A&M offensive lineman Luke Joeckel, appeared in five games in 2013 in backup duty to Johnny Manziel. Joeckel completed 22-of-37 passes for 293 yards and two touchdowns last season. He started the first half of the Aggies' opening game against Rice and threw for 190 yards and one score while Manziel was sidelined due to a suspension. Joeckel's transfer whittles the Aggies' quarterback competition down to sophomore Kenny Hill and true freshman Kyle Allen. A former five-star prospect, Allen was Rivals.com's top pro-style quarterback in the 2014 class. Hill, meanwhile, made offseason headlines last month when he was arrested on a charge of public intoxication.