An important goal of the future $\overline{\rm P}$ANDA Experiment at FAIR (Darmstadt, Germany) is the investigation of the proton structure. Electromagnetic proton form factors parameterize the electric and magnetic structure of protons. They can be experimentally accessed in the time-like region through the annihilation processes $\bar p p \to \ell^+ \ell^- ~(\ell=e,\mu)$, assuming that the interaction takes place through the exchange of one virtual photon. The expected statistical precision for the measurement of proton form factors with $\overline{\rm P}$ANDA for the process $\bar p p \to \ell^+ \ell^- ~(\ell=e,\mu)$ was investigated in the framework of the PANDARoot software for detector simulation and event reconstruction. The signal identification and the suppression of the main background process ($\bar p p \to \pi^+ \pi^-$) is studied. Different methods have been used to generate and analyse the processes of interest. The results show that time-like electromagnetic proton form factors can be measured at $\overline{\rm P}$ANDA with high statistical accuracy over a large kinematical region.