The Dutchman arrived at Stamford Bridge as an assistant manager to Avram Grant last October.
However, Grant was dismissed last month after failing to lead the Blues to either Premier League or UEFA Champions League glory.
He has now taken charge of Greek club Panathinaikos on a two-year contract.
Jose Peseiro resigned as Pana coach in May and Ten Cate is delighted to have been brought in as his replacement.
"In my career I have been used to working at the highest level of competition and that's one of the reasons why I consider this new step to be a great challenge," Ten Cate told Panathinaikos' official website.
"Panathinaikos' organisation, history, ambition and attitude towards football in general match those of the greatest football clubs in Europe."