Sahih Muslim Book 23, Hadith Number 5041.

Chapter : The merit of licking the fingers after taking food and wiping the dish (with fingers) and eating of the fallen mouthful after removing the dirt sticking to it.

‘Abdullah b. Ka’b reported that his father Ka’b narrated to him that Allah’s Messenger (may peace be upon him) used to eat with three fingers and when he had finished (eating), he licked them.