The moves came before the Yankees played Detroit on Tuesday night.
The 34-year-old Hill 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 Boston. He is 24-22 with a 4.75 ERA during 10 seasons in the majors with the Cubs, Baltimore, Boston, Cleveland and the Angels.
The 37-year-old Thornton was 0-3 with a 2.55 ERA in 46 games for the Yankees, pitching 24 2-3 innings.
Yankees manager Joe Girardi says Thornton did well as a lefty specialist. He said Hill could be used in similar situations, and also for multiple innings.