We report the discovery of 3.76 s pulsations from a new burst source near Sgr A* observed by the NuSTAR observatory. The strong signal from SGR J1745-29 presents a complex pulse profile modulated with pulsed fraction 27% ± 3% in the 3-10 keV band. Two observations spaced nine days apart yield a spin-down rate of dot{P} =(6.5 ± 1.4) × 10-12. This implies a magnetic field B = 1.6 × 1014 G, spin-down power dot{E} =5 × 1033 erg s-1, and characteristic age P/2dot{P} =9 × 103 yr for the rotating dipole model. However, the current dot{P} may be erratic, especially during outburst. The flux and modulation remained steady during the observations and the 3-79 keV spectrum is well fitted by a combined blackbody plus power-law model with temperature kT BB = 0.96 ± 0.02 keV and photon index Γ = 1.5 ± 0.4. The neutral hydrogen column density (N H ~ 1.4 × 1023 cm-2) measured by NuSTAR and Swift suggests that SGR J1745-29 is located at or near the Galactic center. The lack of an X-ray counterpart in the published Chandra survey catalog sets a quiescent 2-8 keV luminosity limit of Lx <~ 1032 erg s-1. The bursting, timing, and spectral properties indicate a transient magnetar undergoing an outburst with 2-79 keV luminosity up to 3.5 × 1035 erg s-1 for a distance of 8 kpc. SGR J1745-29 joins a growing subclass of transient magnetars, indicating that many magnetars in quiescence remain undetected in the X-ray band or have been detected as high-B radio pulsars. The peculiar location of SGR J1745-29 has important implications for the formation and dynamics of neutron stars in the Galactic center region.