Approximately 90% of all ophthalmic drug formulations are now applied as eye drops. While eye drops are convenient and well-accepted by patients, similar to 95% of the drug contained in the drops is lost due to absorption through the conjunctiva or through the tear drainage. Ophthalmic drug delivery via contact lenses is more effective because it increases the residence time of the drug in the eye and leads to a larger fractional intake of drug by the cornea. In this paper, we model the drug release from the contact lens into the pre- and postlens tear films and the subsequent uptake by the cornea. The motion of the contact lens, which is driven by the eyelid motion during a blink, enhances the mass transfer in the postlens tear film (POLTF). We use regular perturbation methods to obtain the Taylor dispersion coefficient for mass transfer in the POLTF. The diffusion of drug in the gel is assumed to obey Fick's law, and the diffusion in the gel and the mass transfer in the POLTF are combined to yield an integro-differential equation that is solved numerically by finite difference. Two extreme cases are considered in this paper. The first case corresponds to a rapid breakup of the prelens tear film (PLTF) that prevents drug loss from the anterior lens surface into the PLTF. The second case corresponds to a situation in which the prelens tear film exists at all times and, furthermore, the mixing and the tear drainage in the blink ensure that the concentration in this film is zero at all times. These two cases correspond to the minimum and the maximum loss to the prelens tear film and, thus, represent the highest and the lowest estimations for the fraction of the entrapped drug that diffuses into the cornea. Results show that the dispersion coefficient of the drug in the postlens tear film is unaffected by the release of the drug from the gel. Furthermore, simulation results show that drug delivery from a contact lens is more efficient than drug delivery by drops. The fraction of drug that enters the cornea varies from similar to 70 to 95% for the first case (no flux to the PLTF) and from 20 to 35% for the second case (zero concentration in the PLTF). The model predicts that delivery of pilocarpine by soaked contact lenses is similar to 35 times more efficient than delivery by drops, and this result matches clinical observations.