The 29-year-old Dutchman, who began his career at Ajax, most recently played for Al-Ain in the United Arab Emirates.
Deportivo signed Babel as Joselu, who is on loan from Stoke, faces two months out with a knee injury.
"I'm very excited. It is a dream come true to play in La Liga," Babel told the Deportivo website.
"I feel good but not yet ready to play.
"It is always difficult for a player who has not had a pre-season, but with my experience I will be able to overcome this."
Former Liverpool winger Ryan Babel has joined Spanish side Deportivo La Coruna on a free transfer until the end of 2016.