A high-energy, high-power ultrafast fiber laser system based on spatiotemporal coherent combination is presented. Bursts of eight subsequent chirped-pulse amplification (CPA)-stretched pulses are amplified simultaneously in 16 parallel ytterbium-doped rod-type amplifiers. After spatial and temporal coherent combination of the total 128 amplified pulse replicas into a single pulse, it is compressed in a partially protective-gas-filled CPA compressor. Finally, nearly Fourier-transform-limited pulses with an energy of 32 mJ and a duration of 158 fs are emitted with a repetition rate of 20 kHz and a close to diffraction-limited beam quality.