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 (P) over dot = (6.5 +/- 1.4) x 10(-12). This implies a magnetic field B = 1.6 x 10(14) G, spin-down power (E) over dot = 5 x 10(33) erg s(-1), and characteristic age P/2(P) over dot = 9 x 10(3) yr for the rotating dipole model. However, the current (P) over dot 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 Gamma = 1.5 +/- 0.4. The neutral hydrogen column density (N-H similar to 1.4 x 10(23) 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 less than or similar to 10(32) 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 x 10(35) 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.