Herrera, 19, was 3-4 with a 3.38 ERA in nine starts for Oakland's Class A affiliate in the Midwest League, striking out 35 batters in 50 2/3 innings while issuing just 10 walks.
The Venezuelan was originally signed by the A's in December 2011 for $20,000 and posted a 3.36 ERA in three seasons in their system.
Herrera will report to the Padres' low-A affiliate, the Fort Wayne TinCaps, of the Midwest League and will likely start there on Friday.
In parts of three seasons with the A's, Herrera was 12-12 with a 3.36 ERA in 187 1/3 innings. He had 145 strikeouts and just 43 walks over that stretch.
"We targeted him as a guy we saw in the Arizona rookie league and in the Midwest League," said Padres assistant general manager A.J. Hinch. "He's a good athlete with a good arm and has a good feel for what he's doing. We like the arm and his ability to command the fastball."