A substrate bonding apparatus and a method of bonding substrates, the apparatus including an upper chuck securing a first substrate onto a lower surface thereof such that the first substrate is downwardly deformed into a concave surface profile; a lower chuck arranged under the upper chuck and securing a second substrate onto an upper surface thereof such that the second substrate is upwardly deformed into a convex surface profile; and a chuck controller controlling the upper chuck and the lower chuck to secure the first substrate and the second substrate, respectively, and generating a shape parameter for changing a shape of the second substrate to the convex surface profile from a flat surface profile.