A method for magnetic-equilibria reconstruction in axisymmetric, large-aspect-ratio toroidal plasmas is presented, which takes as input the plasma-pressure and the reduced poloidalmagnetic-field profiles, measured in laboratory coordinates along any chord crossing the magnetic axis, together with suitable boundary conditions. Besides yielding solutions in a closed integral form, with concomitant advantages over the usual sets of nonlinearly coupled differential equations, either for analytical or numerical work, the proposed approach circumvents the need to assume beforehand any relationship between the plasma pressure, the toroidal-magnetic-field pressure, and the poloidal-flux function. This enables magnetic equilibria to be reconstructed directly from experimental data, departing from the accustomed practice of fitting such data over a predefined model by iteratively solving the Grad-Shafranov equation, and therefore reduces the computational effort involved.