The solar eclipse on 11 August 1999 was quite unique due to its totality belt coverage of the territory of central Europe where the facilities for the geophysical monitoring are most dense. Ionospheric and geomagnetic observations during the eclipse allowed us to study the eclipse-induced effects more precisely. A mathematical model based on the classical Ashour-Chapman model is considered to show that the decrease (up to 40%) of the ionospheric total electron content in the region of the totality belt leads finally to geomagnetic disturbances quantitatively dependent on the position of both the quasi-circular spot of the ionospheric conductivity decrease and given geomagnetic observatory location. The model is generalized for the anisotropic ionosphere. The theoretical estimates are compared with observational data from European geomagnetic observatories: F¿rstenfeldbruck, Nagycenk, Tihany, and Hurbanovo, the last one being nearby the totality belt.