His contract with the Bundesliga side was terminated by mutual consent yesterday and the Eredivisie champions have apparently swooped in to sign him on a one-year deal on transfer deadline day.
The Netherlands international is a product of the Ajax youth system and was a key member of the Amsterdam giants first-team for three years before joining Liverpool in 2007.
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Babel’s agent, Winny Haatrecht, revealed the Dutch giants had offered the 25-year-old a contract and said the Amsterdam native is committed to the club and is keen to get his career back on track after failed stints at Liverpool and Hoffenheim.
"Ryan knows the club, the coach and hopes to make a major contribution to the further development of the team," Haatrecht told De Telegraaf.
“[Ajax coach] Frank [de Boer] knows Ryan from his time at the Dutch national team and knows he can use him as a left winger and a striker.
"One benefit is that Ryan recent seasons never been injured."
He added: “There were many clubs interested in Ryan, but Ajax stood out for him. It should be a good partnership."