The use of multi-block copolymers of styrene (S), maleic anhydride (MA), and butyl acrylate (BA) (poly((S-alt-MA)-block-S-block-BA-block-S-block-(S-alt-MA))) synthesized by reversible addition-fragmentation chain transfer (RAFT) polymerization as asphalt modifiers, is reported. Emphasis is placed on the influence of controlled copolymer structures and maleic anhydride content on physical properties, morphology, thermal stability and rheological behavior of asphalt blends. Our results show that the degree of asphalt modification is a function of both, copolymer structure and maleic anhydride content. Rheological, thermal and microstructure analyses reveal that the addition of reactive copolymers increases chemical interactions with asphalt polar fractions. Significant improvement of viscosity, elasticity, and storage stability are observed in the blends with SMA-S-BA-S-SMA copolymers at MA concentrations of 2-6% compared to copolymers without functional groups.