We have prepared epitaxial FePt ${L1}_{0}$ (001) nanoparticles covered with Ag and Pt overlayers and investigated their magnetic behaviors by means of anomalous Hall resistance measurements. The particle shapes are thin oblate spheroids with the aspect ratio (height/diameter) of 1/5. The size is ranging from 1 to 2.5 nm in height and from 5 to 30 nm in diameter. FePt ${L1}_{0}$ nanoparticles show extremely large coercivity ${H}_{c}$ of about 70 kOe at 10 K, which is close to the anisotropy field ${H}_{k}$ of highly ordered FePt ${L1}_{0}.$ This verifies that the very strong magnetic anisotropy ${K}_{u}$ of FePt ${L1}_{0}$ remains even in the size of several atomic layers along the c axis. For a particle diameter of ${D}_{m}<20\mathrm{nm},$ all the magnetic properties, such as the angular dependence of irreversible switching field, the magnitude of ${H}_{c},$ and their temperature dependence, are fully explained by the coherent rotation model, taking the thermal relaxation into account. Although both Ag- and Pt-coated particles follow the coherent rotation model, the latter always exhibits smaller ${H}_{c}$ than the former. Such a decrease in ${H}_{c}$ can be explained by assuming an enhancement of the effective magnetic moment caused by ferromagnetic polarization of Pt atoms at the Pt/FePt interface. As the particle size ${D}_{m}$ exceeds 20 nm, the magnetic behaviors deviate from the ideal coherent rotation model, suggesting that the magnetization reversal mode changes from coherent to incoherent rotation. The critical diameter ${D}_{m}\ensuremath{\sim}20\mathrm{nm}$ at which the reversal mode changes is in good agreement with the critical diameter predicted by the micromagnetic theory.