The anisotropy of the azimuthal distributions of charged particles produced in $\sqrt{{s}_{NN}}=2.76$ TeV PbPb collisions is studied with the CMS experiment at the LHC. The elliptic anisotropy parameter, ${v}_{2}$, defined as the second coefficient in a Fourier expansion of the particle invariant yields, is extracted using the event-plane method, two- and four-particle cumulants, and Lee-Yang zeros. The anisotropy is presented as a function of transverse momentum (${p}_{\mathrm{T}}$), pseudorapidity ($\ensuremath{\eta}$) over a broad kinematic range, $0.3<{p}_{\mathrm{T}}<20$ GeV/c, $|\ensuremath{\eta}|<2.4$, and in 12 classes of collision centrality from 0 to $80%$. The results are compared to those obtained at lower center-of-mass energies, and various scaling behaviors are examined. When scaled by the geometric eccentricity of the collision zone, the elliptic anisotropy is found to obey a universal scaling with the transverse particle density for different collision systems and center-of-mass energies.