The two clubs had already agreed a fee of £2.1million for the defender and Hinkel could make his debut in the derby with Rangers on 2 January.
Celtic have been without a right back following long term injuries to Mark Wilson and Jean Perrier Doumbe, forcing centre half Gary Caldwell to cover the position in recent games.
"Hinkel isn't getting the continuity he needs because he's competing with Daniel Alves, the best right back in the world," Sevilla sports director Ramon Rodriguez told the club website.