A new quantum-voltage-calibrated Johnson noise thermometer was developed at the National Institute of Metrology to demonstrate the electrical approach that determines Boltzmann's constant k, by comparing electrical and thermal noise power. A measurement with an integration period of 19 h and a bandwidth of 638 kHz results in a relative offset of 1 × 10^-6, from the current Committee on Data for Science and Technology value of k, and a type A relative standard uncertainty of 17 × 10^-6. Closely matched noise powers and transmission-line impedances were achieved, and consequently, the quadratic fitting parameters of the ratio spectrum show flat frequency responses with respect to the measurement bandwidth. This flat response produces a dramatically reduced systematic error compared to that of the National Institute of Standards and Technology measurement of k, in which the relative combined uncertainty was dominated by this error.