Dopant atoms are used to control the properties of semiconductors in most electronic devices. Recent advances such as single-ion implantation(1-5) have allowed the precise positioning of single dopants in semiconductors as well as the fabrication of single-atom transistors(6-9), representing steps forward in the realization of quantum circuits(10-14). However, the interactions between dopant atoms have only been studied in systems containing large numbers of dopants, so it has not been possible to explore fundamental phenomena such as the Anderson-Mott transition between conduction by sequential tunnelling through isolated dopant atoms, and conduction through thermally activated impurity Hubbard bands(15-18). Here, we observe the Anderson-Mott transition at low temperatures in silicon transistors containing arrays of two, four or six arsenic dopant atoms that have been deterministically implanted along the channel of the device. The transition is induced by controlling the spacing between dopant atoms. Furthermore, at the critical density between tunnelling and band transport regimes, we are able to change the phase of the electron system from a frozen Wigner-like phase to a Fermi glass by increasing the temperature. Our results open up new approaches for the investigation of coherent transport, band engineering and strongly correlated systems in condensed-matter physics.