The 31-year-old Olivera came to the United States from Cuba in 2015 and has played in just 30 games. He is currently serving an 82-game suspension for violating the league's domestic violence policy that will end on Monday.
Dennis Lin of the San Diego Union-Tribune added that the DFA will not become official until he gets off of the league's suspension list on Tuesday.
The Padres sent veteran right fielder Matt Kemp to the Atlanta Braves, per ESPN.com, as the team was able to shed his big contract.
Per Lin, Olivera was expected to be designated for assignment upon the deal's completion as the Padres continue to shed big-name players in order to rebuild the franchise.
Kemp was owed $21.5 million in each of the next three years through the 2019 season as San Diego also dealt $10.5 million to the Braves to help them deal with his big contract.
San Diego has also parted ways with Fernando Rodney, Melvin Upton Jr, Andrew Cashner, Drew Pomeranz and James Shields this summer.
Olivera though also had a big contract of his own as he signed a six-year, $52.5 million deal with the Los Angeles Dodgers before he was dealt to the Braves. Per USA Today's Bob Nightengale, Olivera is expected to make $25.5 million in the remainder of his deal.
As a player who hit .322 with 96 home runs and 438 RBI in 11 seasons in Cuba, Olivera has failed to live up to the height during his time in the majors.
In his 30 games over two seasons, he's batted .245 with two home runs and 13 RBI.
He began his rehab assignment in July 15 in the minor leagues as he prepared to come back from his suspension, which came after an April 13 arrest outside of a hotel in Washington, D.C., where he was charged with assault and battery of a woman.
Now just days before being eligible to return to the majors, Olivera might have to find a new home to try and get his professional career in the United States on track.