Bridged-ring scaffolds are prevalent in numerous natural products and pharmaceuticals. However, achieving enantioselective construction of these architectures presents a significant challenge, due to the considerable structural strain of the products and the presence of multiple stereocenters. Herein, we report a Pd/Cu co-catalyzed substrate-dependent enantiodivergent tandem Heck/Sonogashira reaction for the synthesis of alkyne-tethered (R,S,S)-bicyclo[3.2.1]octenes and (S,R,R)-benzo-bicyclo[3.2.1]octanes, each featuring one quaternary and two adjacent tertiary stereocenters. Intramolecular cyclization of the resultant bridged-ring skeletons facilitates the stereospecific synthesis of rigid chiral tricyclodecanes and tetracyclotetradecanes. The alkene, alkyne and ester motifs within bicyclo[3.2.1]octenes and benzo-bicyclo[3.2.1]octanes enables a diverse of transformations, providing access to versatile bridged-ring compounds. Preliminary activity assays demonstrate that two of chiral bridged-ring compounds display good inhibitory effects on the cGAS-STING signaling pathway. Mechanistic studies and DFT calculations indicate that reductive elimination is the rate-determining step in tandem Heck/Sonogashira reaction. Furthermore, key factors responsible for the substrate-dependent enantiodivergence are elucidated through DFT calculations.