We present a high-repetition-frequency, diode-pumped, and chirped-pulse amplification system operating at 106 W average output with excellent beam quality (M^2 = 1.3), based on cryogenically cooled Yb:YLF. 1 nJ seed pulses, derived from a mode-locked Ti:sapphire laser, are first amplified to 1 mJ pulse energy at 10 kHz repetition frequency in a regenerative amplifier. The second-stage, multipass amplifier increases the pulse energy to 10.6 mJ, resulting in a spectral width of 2.2 nm. The pulses are compressed to 865 fs in duration, which is 1.26 times the transform limit.