The azimuthal anisotropy of charged particles in Pb-Pb collisions at $\sqrt{{s}_{NN}}=2.76\text{ }\text{ }\mathrm{TeV}$ is measured with the CMS detector at the LHC over an extended transverse momentum (${p}_{\mathrm{T}}$) range up to approximately $60\text{ }\text{ }\mathrm{GeV}/c$. The data cover both the low-${p}_{\mathrm{T}}$ region associated with hydrodynamic flow phenomena and the high-${p}_{\mathrm{T}}$ region where the anisotropies may reflect the path-length dependence of parton energy loss in the created medium. The anisotropy parameter (${v}_{2}$) of the particles is extracted by correlating charged tracks with respect to the event-plane reconstructed by using the energy deposited in forward-angle calorimeters. For the six bins of collision centrality studied, spanning the range of 0--60% most-central events, the observed ${v}_{2}$ values are found to first increase with ${p}_{\mathrm{T}}$, reaching a maximum around ${p}_{\mathrm{T}}=3\text{ }\text{ }\mathrm{GeV}/c$, and then to gradually decrease to almost zero, with the decline persisting up to at least ${p}_{\mathrm{T}}=40\text{ }\text{ }\mathrm{GeV}/c$ over the full centrality range measured.