The development of technologies for the efficient synthesis of innovative antiviral compounds remains an important challenge for modern biotechnology, especially in the context of the recent COVID-19 pandemic. One of the drugs that is currently in the research spotlight for potential anti-SARS-CoV-2 activity is the purine mimetic prodrug compound T-705, also known as favipiravir. Along with a similar compound, T-1105, the activation of T-705 is limited by the low rate of phosphoribosylation, mediated by an enzyme named hypoxanthine-guanine phosphoribosyltransferase (HGPRT). Therefore, the synthesis of phosphoribosylated/ribosylated derivatives of these prodrugs is a viable direction for the discovery and development of antiviral pharmaceuticals. However, the chemical synthesis of such compounds is a complex and laborious process, whereas enzymatic cascades are not feasible because of the narrow HGPRT substrate specificity. Here, we report the successful rational design of an efficient biocatalyst for T-705/T-1105 phosphoribosylation. With two rounds of Thermus thermophilus HB27 HGPRT active site optimization, we have achieved a 325-fold increase in kcat toward the compound T-705 and a 125-fold increase toward T-1105 accompanied by a multifold decrease in KM. The practical applicability of the designed mutant was illustrated through the preparative synthesis of T-705/T-1105 nucleotide derivatives. Our engineered biocatalyst can become a basis for the technologies of enzymatic and chemoenzymatic synthesis of various T-705/T-1105 derivatives with proven antiviral activity. Moreover, our results provide insight into the molecular mechanism of T-705/T-1105 phosphoribosylation, including the experimental evidence explaining the reasons behind the low activity of HGPRT toward these compounds.