The mailman is the Gravity Falls mail carrier.
His first appearance is in "Tourist Trapped," when Soos mentions that he frequently notices odd things in Gravity Falls, like the mailman, whom he believes to be a werewolf. This is neither confirmed nor denied.
He is covered with reddish-brown hair, wears a blue mailman uniform with a hat, and holds a mail bag. His chest hair puffs out of his shirt, he has bushy eyebrows, a beard, and a mustache.