Greenhouses in high latitudes consume vast amounts of energy for heating and supplemental lighting. Light emitting diodes (LEDs) have been suggested as having great potential for reducing greenhouse energy use, as they are extremely efficient at converting electricity to light. However, LEDs emit very little heat, which must be compensated by the greenhouse heating system. Thus, it is unclear how much energy can be saved by LEDs when the need for extra heating is taken into account. This study presents a first analysis of the energy demands for greenhouses transitioning from high-pressure sodium (HPS) to LED lighting, providing a quantification of the total energy savings achieved by LEDs. Model simulations using GreenLight, an open source greenhouse model, were used to examine a wide range of climates, from subtropical China to arctic Sweden, and multiple settings for indoor temperature, lamp intensity, lighting duration, and insulation. In most cases, the total energy saving by transition to LEDs was 10–25%. This value was linearly correlated with the fraction of energy used for lighting before the transition, which was 40–80%. In all scenarios, LEDs reduced the energy demand for lighting but increased the demand for heating. Since energy for lighting and heating is often derived from different origins, the benefits of a transition to LEDs depend on the environmental and financial costs of the available energy sources. The framework provided here can be used to select lighting installations that make optimal use of available energy resources in the most efficient and sustainable manner.