Single-photon detectors operating at visible and near-infrared wavelengths with high detection efficiency and low noise are a requirement for many quantum-information applications. Superconducting transition-edge sensors (TESs) are capable of detecting visible and near-infrared light at the single-photon level and are capable of discriminating between one-and two-photon absorption events; however these capabilities place stringent design requirements on the TES heat capacity, thermometry, and optical detection efficiency. We describe the fabrication and evaluation of a fiber-coupled, photon-number-resolving TES detector optimized for absorption at 1550 and 1310 nm wavelengths. The measured system detection efficiency at 1556 nm is 95 %±2 %, which to our knowledge is the highest system detection efficiency reported for a near-infrared single-photon detector.