Graphene offers great promise to complement the inherent limitations of silicon electronics. To date, considerable research efforts have been devoted to complementary p- and n-type doping of graphene as a fundamental requirement for graphene-based electronics. Unfortunately, previous efforts suffer from undesired defect formation, poor controllability of doping level, and subtle environmental sensitivity. Here we present that graphene can be complementary p- and n-doped by simple polymer coating with different dipolar characteristics. Significantly, spontaneous vertical ordering of dipolar pyridine side groups of poly(4-vinylpyridine) at graphene surface can stabilize n-type doping at room-temperature ambient condition. The dipole field also enhances and balances the charge mobility by screening the impurity charge effect from the bottom substrate. We successfully demonstrate ambient stable inverters by integrating p- and n-type graphene transistors, which demonstrated clear voltage inversion with a gain of 0.17 at a 3.3 V input voltage. This straightforward polymer doping offers diverse opportunities for graphene-based electronics, including logic circuits, particularly in mechanically flexible form.