Field-effect transistors fabricated on graphene grown by chemical vapor deposition (CVD) often exhibit large hysteresis accompanied by low mobility, high positive backgate voltage corresponding to the minimum conductivity point (V_min), and high intrinsic carrier concentration (n₀). In this report, we show that the mobility reported to date for CVD graphene devices on SiO₂ is limited by trapped water between the graphene and SiO₂ substrate, impurities introduced during the transfer process and adsorbates acquired from the ambient. We systematically study the origin of the scattering impurities and report on a process which achieves the highest mobility (μ) reported to date on large-area devices for CVD graphene on SiO₂: maximum mobility (μ_max) of 7800 cm²/(V·s) measured at room temperature and 12 700 cm²/(V·s) at 77 K. These mobility values are close to those reported for exfoliated graphene on SiO₂ and can be obtained through the careful control of device fabrication steps including minimizing resist residue and non-aqueous transfer combined with annealing. It is also observed that CVD graphene is prone to adsorption of atmospheric species, and annealing at elevated temperature in vacuum helps remove these species.