Hyperdoping Si with chalcogens is a topic of great interest due to the strong sub-band-gap absorption exhibited by the resulting material, which can be exploited to develop broadband room-temperature infrared photodetectors using fully Si-compatible technology. Here, we report on the critical behavior of the impurity-driven insulator-to-metal transition in Te-hyperdoped Si layers fabricated via ion implantation followed by nanosecond pulsed-laser melting. Electrical transport measurements reveal an insulator-to-metal transition, which is also confirmed and understood by density functional theory calculations. We demonstrate that the metallic phase is governed by a power-law dependence of the conductivity at temperatures below 25 K, whereas the conductivity in the insulating phase is well described by a variable-range hopping mechanism with a Coulomb gap at temperatures in the range of 2--50 K. These results show that the electron wave function in the vicinity of the transition is strongly affected by the disorder and the electron-electron interaction.