The Dutchman became a free agent after his contract expired at Al-Ain in the United Arab Emirates.
Upon signing for the club, the winger told the club's website: "I'm very excited. It is a dream come true to play in La Liga.
"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".
Babel played 146 games in his time at Liverpool, scoring 22 goals.