Sayyiduna Ibn Abbas (may Allah be pleased with them both) said that his mother, Umm al-Fadl bint al-Harith (may Allah be pleased with her), told him: One day I was passing by the Prophet (peace and blessings be upon him) while he was sitting in the Hijr (of Isma'il), and he said: "O Umm al-Fadl!" I said: At your service, O Messenger of Allah. He (peace and blessings be upon him) said: "You are pregnant with a boy." I said: How can that be, when Quraysh have sworn oaths that no woman shall give birth? He (peace and blessings be upon him) said: "It is as I tell you; when you give birth to him, bring him to me." So when I gave birth to him, I brought him to the Prophet (peace and blessings be upon him). He named him Abdullah, gave him tahnik with his saliva, then said: "Take him away; you will surely find him clever." Then I went to Abbas (may Allah be pleased with him) and told him. He put on his clothes and came to the Prophet (peace and blessings be upon him); he was a handsome, tall man. When the Messenger of Allah (peace and blessings be upon him) saw him, he stood up towards him, kissed him between his eyes, then seated him on his right and said: "This is my uncle; let whoever wishes take pride in his uncle." Sayyiduna Abbas (may Allah be pleased with him) said: O Messenger of Allah, say less (that is, do not praise me so much). He (peace and blessings be upon him) said: "Why should I not say it, when you are my uncle and the remnant of my forefathers, and an uncle is like a father?"
Hadith Referenceالمعجم الكبير للطبراني / باب العين / 10534