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We report NuSTAR and Chandra observations of two X-ray transients, SWIFT J174540.7−290015 (T15) and SWIFT J174540.2−290037 (T37), which were discovered by the Neil Gehrels Swift Observatory in 2016 within r ∼ 1 pc of Sgr A*. NuSTAR detected bright X-ray outbursts from T15 and T37, likely in the soft and hard states, with 3–79 keV luminosities of 8 × 1036 and 3 × 1037 erg s−1, respectively. No X-ray outbursts have previously been detected from the two transients and our Chandra ACIS analysis puts an upper limit of LX ≲ 2 × 1031 erg s−1 on their quiescent 2–8 keV luminosities. No pulsations, significant quasi-periodic oscillations, or type I X-ray bursts were detected in the NuSTAR data. While T15 exhibited no significant red noise, the T37 power density spectra are well characterized by three Lorentzian components. The declining variability of T37 above ν ∼ 10 Hz is typical of black hole (BH) transients in the hard state. NuSTAR spectra of both transients exhibit a thermal disk blackbody, X-ray reflection with broadened Fe atomic features, and a continuum component well described by Comptonization models. Their X-ray reflection spectra are most consistent with high BH spin (a* ≳ 0.9) and large disk density (ne ∼ 1021 cm−3). Based on the best-fit ionization parameters and disk densities, we found that X-ray reflection occurred near the inner-disk radius, which was derived from the relativistic broadening and thermal disk component. These X-ray characteristics suggest the outbursting BH-low-mass X-ray binary scenario for both transients and yield the first BH spin measurements from X-ray transients in the central 100 pc region. [ABSTRACT FROM AUTHOR]