A gossiper is someone who talks eagerly and casually about other people. If you like to spread rumors and hear the latest news about your friends, you might be a gossiper.
When you gossip, you talk enthusiastically about other people's news or business. To do this regularly is to be a gossiper. Gossipers are known for their habits of chattering, filling their friends in on details of people's lives, some true and others based purely on rumors or guesses. The Old English root of both gossip and gossiper is godsibb, originally "godparent" and later "familiar acquaintance" or "person engaging in familiar or idle talk."