The sides reached an agreement on the terms last week before he passed a physical to complete the deal.
Ziegler, who features a submarine-style delivery, posted a 4-7 record with 22 saves while splitting time with the Arizona Diamondbacks and Boston Red Sox last season. The 37-year-old combined for a 2.25 ERA in 69 relief appearances (68 innings).
Incumbent closer A.J. Ramos could have a new setup man in Ziegler, who has a 34-28 career mark with 85 saves in 604 appearances with the Oakland Athletics, Diamondbacks and Red Sox.