Sahih Muslim Book 6, Hadith Number 2520.

Ibn’Abbas (Allah be pleased with both of them) reported that the Messenger of Allah (may peace be upon him) arrived in Medina and found the Jews observing fast on the day of ‘Ashura. The Messenger of Allah (may peace be upon him) said to them: What is the (significance) of this day that you observe fast on it? They said: It is the day of great (significance) when Allah delivered Moses and his people, and drowned the Pharaoh and his people, and Moses observed fast out of gratitude and we also observe it. Upon this the Messenger of Allah (may peace be upon him) said: We have more right, and we have a closer connection with Moses than you have; so Allah’s Messenger (may peace be upon him) observed fast (on the day of ‘Ashura), and gave orders that it should be observed.