We present a linear and nonlinear digital pre-distortion (DPD) tailored to the components of an optical transmitter. The DPD concept uses nonlinear models of the transmitter devices, which are obtained from direct component measurements. While the digital-to-analog converter and driver amplifier are modeled jointly by a Volterra series, the modulator is modeled independently as a Wiener system. This allows for a block-wise compensation of the modulator by a Hammerstein system and a pre-distortion of the electrical components by a second Volterra series. In simulations and extensive experiments, the performance of our approach for nonlinear DPD is compared to an equivalent linear solution as well as to a configuration without any DPD. The experiments were performed using M-ary quadrature-amplitude modulation (M-QAM) formats ranging from 16- to 128-QAM at a symbol rate of 32 GBd. It is shown that the DPD improves the required optical signal-to-noise ratio at a bit error ratio of 2·10 ^-2 by at least 1.2 dB. Nonlinear DPD outperforms linear DPD by an additional 0.9 and 2.7 dB for higher-order modulation formats such as 64-QAM and 128-QAM, respectively.