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 \pm 3 % in the 3 - 10 keV band . Two observations spaced 9 days apart yield a spin-down rate of \dot { P } = ( 6.5 \pm 1.4 ) \times 10 ^ { -12 } . This implies a magnetic field B = 1.6 \times 10 ^ { 14 } G , spin-down power \dot { E } = 5 \times 10 ^ { 33 } erg s ^ { -1 } , and characteristic age P / 2 \dot { P } = 9 \times 10 ^ { 3 } 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 { \it k } T _ { BB } = 0.96 \pm 0.02 keV and photon index \Gamma = 1.5 \pm 0.4 . The neutral hydrogen column density ( N _ { H } \sim 1.4 \times 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 L _ { x } \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } 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 \times 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 .