Chemical functionalization of graphene holds promise for various applications ranging from nanoelectronics to catalysis, drug delivery, and nanoassembly. In many applications it is important to be able to transport adsorbates on graphene in real time. We propose to use electromigration to drive the adsorbate transport across the graphene sheet. To assess the efficiency of electromigration, we develop a tight-binding model of electromigration of an adsorbate on graphene and obtain simple analytical expressions for different contributions to the electromigration force. Using experimentally accessible parameters of realistic graphene-based devices as well as electronic structure theory calculations to parametrize the developed model, we argue that electromigration on graphene can be efficient. As an example, we show that the drift velocity of atomic oxygen covalently bound to graphene can reach ~1 cm/s.