De La Rosa, 29, appeared in four games for Durham and was 0-1 with a 9.00 ERA. He last pitched Wednesday against Charlotte and allowed one run while walking two and striking out two in 1 1/3 innings.
De La Rosa got the news of his promotion after Friday night's game at Gwinnett.
"I've been feeling good, working the kinks out and making an adjustment to Triple-A from playing in big league Spring Training," De La Rosa said. "Just adjusting to hitters and not trying to do too much. Trying to pitch above yourself is just kind of a problem for me."
De La Rosa had two stints with the Rays in 2011, compiling a 9.82 ERA in seven relief appearances.
"The big thing about him is also he adds length," said manager Joe Maddon when asked how De La Rosa would be used. "He can pitch 40 to 60 pitches if necessary. That was important for us today. ... We needed to have some length, and he provides that also."