In the field of quantum metrology, transition matrix elements are crucial for accurately evaluating the black-body radiation shift of the clock transition and the amplitude of the related parity-violating transition, and can be used as probes to test quantum electrodynamic effects, especially at the ${10}^{-3}$–${10}^{-4}$ level. We developed a universal experimental approach to precisely determine the dipole transition matrix elements by using the shelving technique, for the species where two transition channels are involved, in which the excitation pulses with increasing duration were utilized to induce shelving, and the resulting shelving probabilities were determined by counting the scattered photons from the excited ${}^2{P}_{1/2}$ state to the ${}^2{S}_{1/2}$ ground state. Using the scattered photons offers several advantages, including insensitivity to fluctuations in magnetic field, laser intensity, and frequency detuning. An intensity-alternating sequence to minimize detection noise and a real-time approach for background photon correction were implemented in parallel. We applied this technique to a single ${\mathrm{Yb}}^{+}$ ion, and determined the $6p{}^2{P}_{1/2}$-$5d{{}^{2}D}_{3/2}$ transition matrix element 2.9979(20) $e{a}_0$, which indicates an order of magnitude improvement over existing reports. By combining our result with the $6p{}^2{P}_{1/2}$ lifetime of 8.12(2) ns, we extracted the $6s{}^2{S}_{1/2}$-$6p{}^2{P}_{1/2}$ transition matrix element to be 2.4703(31) $e{a}_0$. The accurately determined dipole transition matrix elements can serve as a benchmark for the development of high-precision atomic many-body theoretical methods.