A new method of optical fiber manufacturing has been presented. The fibers are technologically oriented to applications as sensors and components of micro-optics. Unusually to other technologies of optical fibres, here the output preform is assembled from modular optical glass rods of standardized dimensions and shapes. The assembly process gives rectangular, square, hexagonal or round fiber optic preform. Next, the output assembled preform is closed in a vacuum ampoule and pulled to obtain a solid intermediate preform. The intermediate preform can be machined or treated chemically to obtained the eventual fiberoptic mosaic preform. The eventual preform is pulled to obtain a complex soft-glass fiber. Because the output preform is obtained through mosaic assembling from modular rods, we suggest that the technology should bear a name Mosaic Assembling Technology (MAT) of optical fibers and to the fibers we will refer as MOSAIC OPTICAL FIBERS. The greatest advantage of MAT is that it can give fibers of unusual structure for instance with the circular cores and refractive index distribution of non-axial geometry. The same concerns to fiber claddings and to other auxilliary layers, which we will refer to as sensitizing / desensitizing layers. The role of these layers is to sensitize the fiber to useful measurands and simultaneously to desensitize the fiber to harmful environmental reactions. Several basic and more complex forms of mosaic optical fibers have been manufactured to show feasibility of the suggested technology. The major properties of mosaic optical fibers have been presented and debated in context of classical ones.