The electronic band structure governs the electron dynamics in solids. It defines a group velocity and an effective mass of the electronic wave packet. Recent experimental and theoretical studies suggest that an electron acquires the effective mass of its excited state over distances much larger than the lattice period of the solid. Therefore, electron propagation on atomic length scales was typically considered to be free-electron-like. Here, we test this hypothesis by probing attosecond photoemission from a Cu(111) surface. We use attosecond pulse trains in the extreme-ultraviolet (21–33 eV) to excite electrons from two initial bands within the 3d-valence band of copper. We timed their arrival at the crystal surface with a probing femtosecond infrared pulse, and found an upper limit of 350±40 as (1 as=10−18 s) for the propagation time an electron requires to assume the effective mass of its excited state. This observation implies that a final-state Bloch wave packet forms within a travel distance of 5–7 Å, which is at most two atomic layers. Using well-established theory, our measurements demonstrate the importance of the band structure even for atomic-scale electron transport.