The serrodyne principle enables an electromagnetic signal to be frequency shifted by applying a linear phase ramp in the time domain. This phenomenon has been exploited to frequency shift signals in the radiofrequency, microwave and optical regions of the electromagnetic spectrum over ranges of up to a few gigahertz, for example, to analyse the Doppler shift of radiofrequency signals for noise suppression and frequency stabilization. Here we employ this principle to shift the centre frequency of high-power femtosecond laser pulses over a range of several terahertz with the help of a nonlinear multi-pass cell. We demonstrate our method experimentally by shifting the central wavelength of a state-of-the-art 75 W frequency comb laser from 1,030 nm to 1,060 nm and to 1,000 nm. Furthermore, we experimentally show that this wavelength-shifting technique supports coherence characteristics at the few hertz-level while improving the temporal pulse quality. The technique is generally applicable to wide parameter ranges and different laser systems, enabling efficient wavelength conversion of high-power lasers to spectral regions beyond the gain bandwidth of available laser platforms.