Förster-type nonradiative energy transfer (FRET) is one of the primary near-field phenomena and is a useful, fundamental mechanism allowing us to control the excitation energy flow. Using carefully chosen pairs of quantum emitters/absorbers (donors/acceptors), FRET has proved to be essential in a variety of light-generating and -harvesting systems. However, FRET takes place only in a limited spatial range, and its efficiency suffers from an adversely rapidly decreasing profile over the increasing distance between the donor and acceptor. To foster FRET, reaching ultimate levels of efficiency and extending its range, we systematically studied the FRET mechanism by tuning the background medium’s permittivity. The FRET rates of donor–acceptor pairs consisting of a point-like, quasi-0-dimensional quantum dot and quasi-2-dimensional quantum well nanostructures are analytically derived to characterize the change of FRET rates with respect to the medium’s permittivity. The analysis reveals that the FRET rate becomes singular when the permittivity approaches zero and there is a fixed value for the point-like and all other nanostructures, respectively. By setting the medium’s relative permittivity to realistic values near the singular point, which can be realized by a digital metamaterial approach, ultrahigh FRET rates and thereby ultraefficient FRET-based systems are achievable.