Encoding electronic functionality into nanoscale elements during chemical synthesis has been extensively explored over the past decade as the key to developing integrated nanosystems(1) with functions defined by synthesis(2-6). Graphene(7-12) has been recently explored as a two-dimensional nanoscale material, and has demonstrated simple device functions based on conventional top-down fabrication(13-20). However, the synthetic approach to encoding electronic functionality and thus enabling an entire integrated graphene electronics in a chemical synthesis had not previously been demonstrated. Here we report an unconventional approach for the synthesis of monolithically integrated electronic devices based on graphene and graphite. Spatial patterning of heterogeneous metal catalysts permits the selective growth of graphene and graphite, with a controlled number of graphene layers. Graphene transistor arrays with graphitic electrodes and interconnects were formed from the synthesis. These functional, all-carbon structures were transferable onto a variety of substrates. The integrated transistor arrays were used to demonstrate real-time, multiplexed chemical sensing and more significantly, multiple carbon layers of the graphene-graphite device components were vertically assembled to form a three-dimensional flexible structure which served as a top-gate transistor array. These results represent substantial progress towards encoding electronic functionality through chemical synthesis and suggest the future promise of one-step integration of graphene-graphite based electronics.