The moves came before the Yankees played the Detroit Tigers on Tuesday night.
Hill, 34, pitched four games at Triple-A Scranton/Wilkes-Barre, striking out 10 in four innings without allowing a run.
Hill pitched two games in the majors this year for the Los Angeles Angels and also was in the minors with the Boston Red Sox. He is 24-22 with a 4.75 ERA during 10 seasons in the majors with the Cubs, Baltimore Orioles, Red Sox, Cleveland Indians and Angels.
Yankees manager Joe Girardi said Thornton did well as a lefty specialist and that Hill could be used in similar situations and also for multiple innings.