Tubular joints are important connecting parts of a welded steel tube structure. The S-N curves based on the hot spot stress (HSS) method are often used to evaluate the fatigue life of tubular joints in practical engineering. The stress concentration factor (SCF) is a key parameter to calculate HSS. In this paper, stress concentration tests of hollow-section and concrete-filled double-skin tubular (CFDST) K-joints were carried out, respectively, and then finite element models of K-joints considering the weld were established. The developed models were validated with the experimental results. The influence of key geometrical parameters, such as the diameter ratio of brace to chord β, the diameter to thickness ratio of chord γ, the wall thickness ratio of brace to chord τ, brace angle θ, and hollow section ratio ζ on the distribution and key position of SCFs along the weld toe, was discussed. Parametric studies were conducted to obtain the calculating equations for the SCF values of CFDST K-joints. The results demonstrate that infill concrete can effectively reduce SCFs along the weld on the chord. When the hollow section ratio was reduced to 0.317, the SCF was reduced by 77.2%. Notably, the SCF reduction rate was sensitive to γ and θ, with a decrease observed as γ increased. The hollow section ratio ζ had a less pronounced effect on SCF distribution patterns, but as ζ decreased, the chord’s stiffness improved, suggesting a potential approach to enhance joint performance. The distribution of SCFs is similar for joints of the same type but different geometric configurations. The innovatively integrated hollow section ratio in the CFDST design equation significantly simplifies and enhances the precision of SCF calculations for CFDST K-joints.