The Tigers agreed to part company with the Guinea international seven days ago on the grounds he wanted to go home to his family in France.
In a new statement, the club said it would receive "nominal compensation".
Even so, the statement on the club website said Zayatte, who gave up a salary of around £20,000 a week with Hull, left with the club's best wishes and regards for his future.
His departure came as a shock to manager Nigel Pearson, who confirmed he would be looking to strengthen his squad's defensive options.
Source: BBC Sport