The deal was announced shortly before the Athletics faced the Orioles in the finale of a three-game series. The 29-year-old Kottaras will join the A's in Oakland on Monday.
Kottaras hit .209 with three homers and 12 RBIs in 58 games with Milwaukee this season. The left-handed hitter was designated for assignment on Thursday to make room for catcher Jonathan Lucroy.
"I really don't know much about him," Oakland manager Bob Melvin said. "I've seen some of the numbers, and know he has a high on-base (percentage) for a guy that's hitting 200-something."
With 29 walks, Kottaras had an OBP of .409 with the Brewers in 2012.
Over five seasons in the big leagues, Kottaras is batting .221 with 18 homers and 65 RBIs in 222 games. Originally drafted by San Diego in the 20th round of the 2002 draft, Kottaras was a member of the 2004 Greek Olympic team.
De Los Santos, 26, spent most of the year at Triple-A Sacramento, where he was 1-3 with a 7.25 ERA in 28 relief appearances. The right-hander began the season on Oakland's Opening Day roster and had a 3.00 ERA in six games before being optioned on April 24.
He went 3-2 with a 4.32 ERA in 34 games with the A's last year.