In this paper, we first propose a novel design-for-testability approach based on M-testability conditions for module-level systolic fast Fourier transform (FFT) arrays. Our M-testability conditions guarantee 100% single-module-fault testability with a minimum number of test patterns. Based on this testable design, fault-tolerant approaches at the bit level and the multiply-subtract-add (MSA) module level are proposed, respectively. If the reconfiguration is performed at the bit level, then the FFT/sub BIT/ network is constructed. Two types of reconfiguration schemes (Type-I FFT/sub MSA/ and Type-II FFT/sub MSA/) are proposed at the MSA module level. Since both the design for testability (DFT) and the design for yield (DFY) issues are considered at the same time for all these proposed approaches, the resulting architectures are simpler as compared with previous works. The reliability of the FFT system increases significantly. The hardware overhead is low-about 12% and 1/2N for the FFT/sub BIT/ network and the Type-II FFT/sub MSA/ network, respectively. An experimental chip is also implemented to verify our approaches. Reliabilities and hardware overhead are also evaluated and compared with previous works.