We report that a nickel catalyst system with a modified 1,1′‐spirobiindane‐7,7′‐diol‐phosphoramidite (SPINOL) as the chiral ligand can enable the coupling of tertiary cyclobutenols and arylboroxines in an enantioconvergent manner, providing cyclobutenes with an all‐carbon quaternary stereocenter in good yields (up to 84 % yield) with excellent enantioselectivities (up to >99 % ee). Moreover, the catalytic system can be applied in the kinetic resolution of cyclobutenols under slightly modified conditions, giving enantioenriched tertiary cyclobutenols with an s factor of up to >200. The reaction uses free hydroxyl groups as the leaving group without additional activation while the strained ring remains untouched. Preliminary mechanistic studies reveal that the inherent discrepant reactivity of the two enantiomers is the key to the controllable enantioconvergent and kinetic resolution process.