In this study, we investigated the exciton binding energy and interband transition between the electron and heavy-hole for the single and double quantum wells which have different hyperbolic-type potential functions subject to electric, magnetic, and non-resonant intense laser fields. The results obtained show that the geometric shapes of the structure and the applied external fields are very effective on the electronic and optical properties. In the absence of the external fields, the exciton binding energy is a decreasing function of increasing well sizes except for the strong confinement regime. Therefore, for all applied external fields, the increase in the well widths produces a red-shift at the absorption peak positions. The magnetic field causes an increase in the exciton binding energy and provides a blue-shift of the absorption peak positions corresponding to interband transitions. The effect of the electric field is quite pronounced in the weak confinement regime, it causes localization in opposite directions of the quantum wells of the electron and hole, thereby weakening the Coulomb interaction between them, causing a decrease in exciton binding energy, and a red-shift of the peak positions corresponding to the interband transitions. Generally, an intense laser field causes a decrease in the exciton binding energy and produces a red-shift of the peak positions corresponding to interband transitions.