The combination of quantum teleportation and quantum memory of photonic qubits is essential for future implementations of large-scale quantum communication and measurement-based quantum computation. Both steps have been achieved separately in many proof-of-principle experiments, but the demonstration of memory-built-in teleportation of photonic qubits remains an experimental challenge. Here, we demonstrate teleportation between photonic (flying) and atomic (stationary) qubits. In our experiment, an unknown polarization state of a single photon is teleported over 7m onto a remote atomic qubit that also serves as a quantum memory. The teleported state can be stored and successfully read out for up to 8s. Besides being of fundamental interest, teleportation between photonic and atomic qubits with the direct inclusion of a readable quantum memory represents a step towards an efficient and scalable quantum network.