We report the detection of a new TeV gamma-ray source, VER J0521+211, based on observations made with the VERITAS imaging atmospheric Cherenkov telescope array. These observations were motivated by the discovery of a cluster of >30GeV photons in the first year of Fermi-LAT observations. VER J0521+211 is relatively bright at TeV energies, with a mean photon flux of 1.93 +/- 0.13_stat +/- 0.78_sys 10^-11 cm-2 s-1 above 0.2 TeV during the period of the VERITAS observations. The source is strongly variable on a daily timescale across all wavebands, from optical to TeV, with a peak flux corresponding to ~0.3 times the steady Crab Nebula flux at TeV energies. Follow-up observations in the optical and X-ray bands classify the newly-discovered TeV source as a BL Lac-type blazar with uncertain redshift, although recent measurements suggest z=0.108. VER J0521+211 exhibits all the defining properties of blazars in radio, optical, X-ray, and gamma-ray wavelengths.