Sayyiduna Abdullah bin Mas'ud (may Allah be pleased with him) reports that the Messenger of Allah (peace and blessings be upon him) said: "The world will not come to an end until a man from my Ahl al-Bayt becomes a ruler, whose name will correspond to my name. He will fill the earth with justice and fairness just as it had previously been filled with oppression and injustice."
Related hadith on this topic