The paper derives an analytically closed-form solution for the optimal weighted-least-squares (WLS) design of variable fractional-delay (VFD) FIR digital filters through exploiting coefficient symmetry and analytically closed-form integrals. The resulting closed-form design is optimal because neither numerical integrals nor parameter discretizations are used in the design process. A design example is given to illustrate that the analytically optimal WLS design method can achieve better design results with significantly reduced computational cost and filter complexity as compared with the existing WLS design methods.