COVID-19 is a global pandemic caused by the SARS-CoV-2 coronavirus. T cells play a key role in the adaptive antiviral immune response by killing infected cells and facilitating the selection of virus-specific antibodies. However, neither the dynamics and cross-reactivity of the SARS-CoV-2-specific T-cell response nor the diversity of resulting immune memory is well understood. In this study, we use longitudinal high-throughput T-cell receptor (TCR) sequencing to track changes in the T-cell repertoire following two mild cases of COVID-19. In both donors, we identified CD4+ and CD8+ T-cell clones with transient clonal expansion after infection. We describe characteristic motifs in TCR sequences of COVID-19-reactive clones and show preferential occurrence of these motifs in publicly available large dataset of repertoires from COVID-19 patients. We show that in both donors, the majority of infection-reactive clonotypes acquire memory phenotypes. Certain T-cell clones were detected in the memory fraction at the pre-infection time point, suggesting participation of pre-existing cross-reactive memory T cells in the immune response to SARS-CoV-2.