SARS-CoV-2 mRNA vaccines have shown remarkable efficacy, especially in preventing severe illness and hospitalization. However, the emergence of several variants of concern and reports of declining antibody levels have raised uncertainty about the durability of immune memory following vaccination. In this study, we longitudinally profiled both antibody and cellular immune responses in SARS-CoV-2 naive and recovered individuals from pre-vaccine baseline to 6 months post-mRNA vaccination. Antibody and neutralizing titers decayed from peak levels but remained detectable in all subjects at 6 months post-vaccination. Functional memory B cell responses, including those specific for the receptor binding domain (RBD) of the Alpha (B.1.1.7), Beta (B.1.351), and Delta (B.1.617.2) variants, were also efficiently generated by mRNA vaccination and continued to increase in frequency between 3 and 6 months post-vaccination. Notably, most memory B cells induced by mRNA vaccines were capable of cross-binding variants of concern, and B cell receptor sequencing revealed significantly more hypermutation in these RBD variant-binding clones compared to clones that exclusively bound wild-type RBD. Moreover, the percent of variant cross-binding memory B cells was higher in vaccinees than individuals who recovered from mild COVID-19. mRNA vaccination also generated antigen-specific CD8+ T cells and durable memory CD4+ T cells in most individuals, with early CD4+ T cell responses correlating with humoral immunity at later timepoints. These findings demonstrate robust, multi-component humoral and cellular immune memory to SARS-CoV-2 and current variants of concern for at least 6 months after mRNA vaccination. Finally, we observed that boosting of pre-existing immunity with mRNA vaccination in SARS-CoV-2 recovered individuals primarily increased antibody responses in the short-term without significantly altering antibody decay rates or long-term B and T cell memory. Together, this study provides insights into the generation and evolution of vaccine-induced immunity to SARS-CoV-2, including variants of concern, and has implications for future booster strategies.