Santos, 31, started the season with the Dodgers and posted a 4.73 ERA in 12 appearances before being designated for assignment on May 27. Santos elected free agency and inked a Minor League deal with the Yankees on Tuesday.
"I think if I can come and establish what I know I can do, and hopefully what the Yankees believe I can do, it'll be a good fit," said Santos, who posted 30 saves for the White Sox in 2011.
Santos is filling a roster spot vacated by right-hander Esmil Rogers, who was outrighted to Triple-A Scranton/Wilkes-Barre after Friday's 11-3 loss to the Orioles and is deciding whether to accept that assignment.