The deal, first reported by the Atlanta Journal-Constitution, will become official once both players have completed their physicals.
Olivera, a 31-year-old Cuban defector, is eligible to return Monday from an 82-game suspension for violating Major League Baseball's domestic-violence policy. The suspension, which is retroactive to April 30, stemmed from his April 13 arrest on assault and battery charges at a hotel outside Washington, D.C.
The Braves acquired Olivera last summer in a trade with the Los Angeles Dodgers, who signed him to a six-year, $62.5 million contract before the 2015 season. He is hitting .211 with no homers and 2 RBIs in six games this season.
Kemp, 31, hasn't lived up to his All-Star form since being traded to San Diego two seasons ago. This season, he is hitting .265 with 23 home runs and 69 RBIs, but has posted a .285 on-base percentage.
He signed an eight-year, $160 million deal with the Dodgers in 2012.
Saturday's trade is the latest among a series of deals the Padres have made in the past two months as they move to rebuild.
Since June, they have traded away four starting pitchers, sending All-Star left-hander Drew Pomeranz to the Boston Red Sox, James Shields to the Chicago White Sox, and Andrew Cashner and Colin Rea to the Miami Marlins.