We have developed a systematic design process for recently proposed slanted grating couplers (SGCs) that operates in the strong coupling regime. Based on rigorous analysis of SGC properties, this design process utilizes the k-vector diagram and a rigorous grating leaky-mode solver to intentionally enforce the phase-match and Bragg conditions. We demonstrate that the resultant SGC designs have performance similar to those obtained by parallel micro-genetic algorithm \left(\text{μGA}\right) optimization with the two-dimensional finite-difference time-domain (2D FDTD) method. Only two 2D FDTD simulations are necessary in the later stages of our systematic design process. Therefore the time saving is tremendous compared to a \text{μGA} 2D FDTD design tool, which can require thousands of individual 2D FDTD simulation runs. We illustrate the utility of our new systematic design process with an embedded slanted grating coupler example.