Noncovalent functionalization via physisorption of organic molecules provides a scalable approach for modifying the electronic structure of graphene while preserving its excellent carrier mobilities. Here we investigated the physisorption of long-chain acenes, namely, hexacene and its fluorinated derivative perfluorohexacene, on bilayer graphene for tunable graphene devices using first-principles methods. We find that the adsorption of these molecules leads to the formation of localized states in the electronic structure of graphene close to its Fermi level, which could be readily tuned by an external electric field in the range of ±3 eV/nm. The electric field not only creates a variable band gap as large as 250 meV in bilayer graphene, but also strongly influences the charge redistribution within the molecule−graphene system. This charge redistribution is found to be weak enough not to induce strong surface doping, but strong enough to help preserve the electronic states near the Dirac point of graphene. Our results further highlight graphene’s potential for selective chemical sensing of physisorbed molecules under the external electric fields.