Sayyiduna Ibn Abbas (may Allah be pleased with them both) narrated that the Prophet (peace and blessings be upon him) arrived and saw that the Jews fasted on the day of Ashura. He (peace and blessings be upon him) asked: "What is the matter with this day?" He was told: "It is the day on which Allah saved Musa (peace be upon him) and drowned the enemy of the Children of Israel, so we are more entitled to Musa (peace be upon him)." So he (peace and blessings be upon him) fasted on that day and ordered that it be fasted.
Hadith Referenceالمعجم الكبير للطبراني / باب العين / 12310