The deal, first reported by the Atlanta Journal-Constitution, will become official once both players have completed their physicals.
The Padres are sending $ 10.5 million to the Braves as part of the trade, a source said.
Olivera, a 31-year-old Cuban defector, is eligible to return Tuesday 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 two 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 Kemp 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.
Information from ESPN’s Jim Bowden was used in this report.