In this Letter we report on an all-optical-fiber approach to the generation of ultra-low-noise microwave signals. We make use of two erbium fiber mode-locked lasers phase locked to a common ultrastable laser source to generate an 11.55 GHz signal with an unprecedented relative phase noise of -111 dBc/Hz at 1 Hz from the carrier. The residual frequency instability of the microwave signals derived from the two optical frequency combs is below 2.3x10(-16) at 1 s and about 4x10(-19) at 6.5x10(4) s (in 5 Hz bandwidth, three days of continuous operation).