We have studied the influence of a terahertz (THz) electric field and a magnetic field on the optical absorption in quantum wells. The studies show that the absorption spectrum becomes much richer in the presence of a THz field and a magnetic field. In a growth-direction polarized THz field, the main features of the quantum-confined Stark effect, such as the red-shift of the absorption edge, the reduction in the magnitude of the main excitonic peaks, and the appearance of additional absorption peaks due to transitions which are forbidden in the absence of a DC field, are retained. In addition, new asymmetric replicas emerge around these peaks. The perpendicular magnetic field leads to quantization of the in-plane motion, and thus enhances the main excitonic peaks and shifts the peaks to the blue, and discretizes the continuum of the absorption spectrum. The magnetic field may leads to the merging or broadening of peaks and replicas.