We report a high-power picosecond optical parametric oscillator (OPO) synchronously pumped by a Yb fiber laser at $1.064\mathrm{\mu m}$ , providing $11.7\mathrm{W}$ of total average power in the near to mid-IR at 73% extraction efficiency. The OPO, based on a $50\mathrm{mm}$ MgO:PPLN crystal, is pumped by $20.8\mathrm{ps}$ pulses at $81.1\mathrm{MHz}$ and can simultaneously deliver $7.1\mathrm{W}$ of signal at $1.56\mathrm{\mu m}$ and $4.6\mathrm{W}$ of idler at $3.33\mathrm{\mu m}$ for $16\mathrm{W}$ of pump power. The oscillator has a threshold of $740\mathrm{mW}$ , with maximum signal power of $7.4\mathrm{W}$ at $1.47\mathrm{\mu m}$ and idler power of $4.9\mathrm{W}$ at $3.08\mathrm{\mu m}$ at slope efficiencies of 51% and 31%, respectively. Wavelength coverage across $1.43–1.63\mathrm{\mu m}$ (signal) and $4.16–3.06\mathrm{\mu m}$ (idler) is obtained, with a total power of ~11 W and an extraction efficiency of ~68%, with pump depletion of ~78% maintained over most of the tuning range. The signal and idler output have a single-mode spatial profile and a peak-to-peak power stability of $\pm 1.8\%$ and $\pm 2.9\%$ over $1\mathrm{h}$ at the highest power, respectively. A signal pulse duration of $17.3\mathrm{ps}$ with a clean single-peak spectrum results in a time-bandwidth product of ~1.72, more than four times below the input pump pulses.