Trade rumors circulated on Saturday, before the move was officially announced on Sunday.
Kottaras was hitting .209 and had 24 strikeouts in 119 plate appearances prior to being designated for assignment by the Brewers on Thursday.
The backup catcher will provide some power for Oakland from the left side of the plate .Though his batting average is hovering near the Mendoza line, his on-base percentage of .409 might have been enough for the A's to see him as an offensive weapon.
De Los Santos appeared in six games for the A's in 2012 and holds 3.00 ERA.
Oakland has yet to announce who will be taken off of the 25-man roster to make room for Kottaras, but catcher Derek Norris is a likely candidate.