We report the detection of pulsed gamma-rays from the young, spin-powered radio pulsar PSR J2021+3651 using data acquired with the Large Area Telescope (LAT) on the Fermi Gamma-ray Space Telescope (formerly GLAST). The light curve consists of two narrow peaks of similar amplitude separated by 0.468 +/- 0.002 in phase. The first peak lags the maximum of the 2 GHz radio pulse by 0.162 +/- 0.004 +/- 0.01 in phase. The integral gamma-ray photon flux above 100 MeV is (56 +/- 3 +/- 11) x 10^{-8} /cm2/s. The photon spectrum is well-described by an exponentially cut-off power law of the form dF/dE = kE^{-\Gamma} e^(-E/E_c) where the energy E is expressed in GeV. The photon index is \Gamma = 1.5 +/- 0.1 +/- 0.1 and the exponential cut-off is E_c = 2.4 +/- 0.3 +/- 0.5 GeV. The first uncertainty is statistical and the second is systematic. The integral photon flux of the bridge is approximately 10% of the pulsed emission, and the upper limit on off-pulse gamma-ray emission from a putative pulsar wind nebula is <10% of the pulsed emission at the 95% confidence level. Radio polarization measurements yield a rotation measure of RM = 524 +/- 4 rad/m^2 but a poorly constrained magnetic geometry. Re-analysis of Chandra data enhanced the significance of the weak X-ray pulsations, and the first peak is roughly phase-aligned with the first gamma-ray peak. We discuss the emission region and beaming geometry based on the shape and spectrum of the gamma-ray light curve combined with radio and X-ray measurements, and the implications for the pulsar distance. Gamma-ray emission from the polar cap region seems unlikely for this pulsar.Read less <