We theoretically and experimentally investigate wavelength tuning of synchronously pumped optical parametric oscillators (OPOs) on changing the cavity length or the pump-repetition rate. Conditions for rapid and wide-range wavelength access are derived. Using an OPO pumped directly by a mode-locked diode-laser master-oscillator power-amplifier (MOPA) system, an all-electronically controlled access to near- and mid-infrared wavelengths is demonstrated. The singly (signal) resonant OPO is based on periodically poled lithium niobate (PPLN) and emits 8 ps idler pulses at a repetition rate of 2.5 GHz in the wavelength range 1986 to 2348 nm (signal: 1530 to 1737 nm). Wavelength tuning over 114 nm (signal) and 189 nm (idler) is achieved solely by electronically varying the repetition rate of the diode-laser oscillator over 720 kHz. By controlling the repetition rate with a programmable driver, an arbitrary emission sequence of the OPO on two wavelength channels is generated, with access times as short as 10 μs. 11 OPO wavelengths equally spaced in the range 1627–1689 nm (signal) or 2054–2154 nm (idler) could be addressed.