The 33-year-old former Spain youth international arrives as a free agent after playing for Deportivo La Coruna, who were relegated from the top flight last season.
"I am aware that Atletico have a great keeper but I come to do my work, to compete and to try and help the team," Aranzubia, who has played more than 300 La Liga matches in spells with Athletic Bilbao and Deportivo, told reporters.
First-choice Courtois, who won Spain's "Zamora" trophy for conceding the fewest goals in the top flight last season, is spending a third season on loan at Atletico from Chelsea.
Diego Simeone's side finished third in La Liga last season to qualify for the Champions League group stages.
The King's Cup winners start their domestic league campaign at Sevilla on Sunday and host La Liga champions Barcelona in the Spanish Super Cup first leg the following Wednesday.
(Reporting by Mark Elkington, editing by Ken Ferris)
