Gott was 4-1 with a 1.20 ERA for the Wildcats in 2013, striking out 35 batters with just five walks as opponents hit .235 against him.
"Great performance track record and someone we think has the mentality to pitch in the back end of the bullpen," said Padres director of scouting Billy Gasparino.
Gott's 23 saves in three seasons made him the all-time leader in Kentucky history, and the Padres like his live arm with a fastball that reaches 95 mph.
He has appeared on the National College Baseball Writers Assocation's "Stopper of the Year" watch list twice, given annually to the country's best reliever.
Jamal Collier is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.