We demonstrate a power-scalable concept for high-power all-solid-state femtosecond lasers, based on passive mode locking of Yb:YAG thin disk lasers with semiconductor saturable-absorber mirrors. We obtained 16.2 W of average output power in pulses with 730-fs duration, 0.47-muJ pulse energy, and 560-kW peak power. This is to our knowledge the highest average power reported for a laser oscillator in the subpicosecond regime. Single-pass frequency doubling through a 5-mm-long lithium triborate crystal (LBO) yields 8-W average output power of 515-nm radiation.