The Dodgers signed Sauer to a minor-league contract Monday that includes an invitation to spring training, Kiley McDaniel of ESPN.com reports.
The Yankees received Sauer as a Rule 5 Draft return from the Royals on Sunday.
Sauer was designated for assignment by the Royals on Monday.
Manager Matt Quatraro informed Sauer he made the Royals' Opening Day roster, Anne Rogers of MLB.com reports Saturday.
Sauer has allowed two runs (one earned) on seven hits and three walks while striking out eight over six innings across four Cactus League games.
Sauer was selected by the Royals in the Rule 5 Draft on Wednesday, Chris Kirschner of The Athletic reports.
Double-A Somerset reinstated Sauer (forearm) from its 7-day injured list Wednesday.
Sauer (forearm) retired just two hitters and allowed five runs (four earned) on two hits and one walk while striking out one in a rehab outing Monday for the Yankees' rookie-level Florida Complex League affiliate.
Sauer recorded 17 strikeouts over eight innings for Double-A Somerset in a game against New Hampshire on Thursday.
Sauer will open the year in extended spring training, MLB.com's Jim Callis reports.