Ibn Abbas reported: The Messenger of Allah, peace and blessings be upon him, came to Medina and he found the Jews fasting the day of Ashura. The Prophet said, “What is this day you are fasting?” They said, “This is a great day in which Allah saved Moses and his people, and He drowned Pharaoh and his people. Moses fasted on it due to gratitude, so we also fast on it.” The Prophet said, “We have more right to it and we are closer to Moses than you.” So the Prophet fasted the day of Ashura and he commanded fasting on it.

Source: Sahih Bukhari 3216, Sahih Muslim 1130