We present a derivation of the electron's mass from our experiment on the electronic g factor in ¹²C⁵⁺ and ¹⁶O⁷⁺ together with the most recent quantum electrodynamical predictions. The value obtained from ¹²C⁵⁺ is m_e=0.0005485799093(3) u, that from oxygen is m_e=0.0005485799092(5) u. Both values agree with the currently accepted one within 1.5 standard deviations but are four respectively two-and-a-half times more precise. The contributions to the uncertainties of our values and perspectives for the determination of the fine-structure constant α by an experiment on the bound-electron g factor are discussed.