A metal interconnect structure provides high adhesive strength between copper atoms in a copper-containing structure and a self-aligned copper encapsulation layer, which is selectively deposited only on exposed copper surfaces. A lower level metal interconnect structure comprises a first dielectric material layer and a copper-containing structure embedded in a lower metallic liner. After a planarization process that forms the copper-containing structure, a material that forms Cu—S bonds with exposed surfaces of the copper-containing structure is applied to the surface of the copper-containing structure. The material is selectively deposited only on exposed Cu surfaces, thereby forming a self-aligned copper encapsulation layer, and provides a high adhesion strength to the copper surface underneath. A dielectric cap layer and an upper level metal interconnect structure can be subsequently formed on the copper encapsulation layer.