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We report an all-fiber, high-power, low-noise amplifier system seeded by an all-normal-dispersion-mode-locked Yb-doped fiber laser oscillator. Up to 10.6 W of average power is obtained at a repetition rate of 43 MHz with diffraction-limited beam quality. Amplified pulses are dechirped to sub-160-fs duration in a grating compressor. It is to our knowledge the first high-power source of femtosecond pulses with completely fiber-integrated amplification comprising commercially available components. Long-term stability is excellent. Short-term stability is characterized and an integrated laser intensity noise of <0.2% is reported. We also conclude that all-normal dispersion fiber oscillators are low-noise sources, suitable as seed for fiber amplifiers. Detailed numerical modeling of both pulse generation in the oscillator and propagation in the amplifier provide very good agreement with the experiments and allow us to identify its limitations.