We propose a piezoelectric transducer-(PZT-) based optoelectronic frequency synchronizer to control simultaneously change in the repetition rate, the relative pulse delay, and the phase noise of a passively mode-locked femtosecond Ti:sapphire laser with an intracavity saturable Bragg reflector absorber with respect to an electronic frequency reference. An optoelectronic phase-locked-loop-based PZT feedback controller with a proportional, integral, and differential (PID) circuit and a tunable voltage regulator is designed to achieve frequency synchronization, phase-noise suppression, and delay-time tuning. When the controlling voltage is tuned from -2.6 to 2.6 V, the maximum pulse-delay range, tuning slope, and tuning resolution of the laser pulse-train are 11.3 ns, 2.3 ps/mV, and 1.2 ps, respectively. Setting the gain constant of the PID circuit at 10 or larger causes the delay-time tuning function to be linearly proportional to the controlling voltage. In the delay-time tuning mode the uncorrelated single-side-band phase-noise density of the frequency-synchronized laser is approximately -120 dBc/Hz at an offset frequency of 5 kHz, which is only 7 dBc/Hz higher than that of the electrical frequency reference. The proposed system also supports linear,continuous switching,and programmable control of the delay time of Ti:sapphire laser pulses when they are frequency synchronized to external reference clocks.