We report the discovery of very high energy gamma-ray emission from the direction of the SNR G54.1+0.3 using the VERITAS ground-based gamma-ray observatory. The TeV signal has an overall significance of 6.8$\sigma$ and appears point-like given the 5$^{arcminute}$ resolution of the instrument. The integral flux above 1 TeV is 2.5% of the Crab Nebula flux and significant emission is measured between 250 GeV and 4 TeV, well described by a power-law energy spectrum dN/dE $\sim$ E$^{-\Gamma}$ with a photon index $\Gamma= 2.39\pm0.23_{stat}\pm0.30_{sys}$. We find no evidence of time variability among observations spanning almost two years. Based on the location, the morphology, the measured spectrum, the lack of variability and a comparison with similar systems previously detected in the TeV band, the most likely counterpart of this new VHE gamma-ray source is the PWN in the SNR G54.1+0.3. The measured X-ray to VHE gamma-ray luminosity ratio is the lowest among all the nebulae supposedly driven by young rotation-powered pulsars, which could indicate a particle-dominated PWN.