We present here a bottom-up approach for realizing on-chip on-demand batteries starting out with chemical vapor deposition-grown graphene. Single graphene monolayers contacted by electrode lines on a silicon chip serve as electrodes. The anode and cathode are realized by electrodeposition of zinc and copper respectively onto graphene, leading to the realization of a miniature graphene-based Daniell cell on a chip. The electrolyte is housed partly in a gel and partly in liquid form in an on-chip enclosure molded using a 3d printer or made out of poly (dimethylsiloxane). The realized batteries provide a stable voltage (similar to 1.1 V) for many hours and exhibit capacities as high as 15 mu Ah, providing enough power to operate a pocket calculator. The realized batteries show promise for deployment as on-chip power sources for autonomous systems in lab-on-a-chip or biomedical applications.