While partial energy transitions have been observed in the past, the complete transition of a fossil-based energy system to a sustainable energy one is historically unprecedented on a large scale. Switching from an economy based on energy stocks to one based on energy flows requires a social paradigm shift. This paper defines Sustainable Energy Transition (SET) and introduces a set of five propositions that prescribe its sustainability. The propositions are comprehensive, spanning environmental constraints, resource availability, equity, and the transition dynamics from an energy and economic accounting perspective aimed at addressing all three pillars of sustainability. In order to rigorously define the constraints of SET a theoretical energy economy framework is introduced along with the concept of the renewable energy investment ratio. The paper concludes with a practical application of the SET propositions on the global energy system and identifies an order of magnitude underinvestment in the renewable energy investment ratio in comparison to the estimated level needed for a controlled transition that satisfies all propositions. The option of drastically increasing this ratio in the future may not be available as it would reduce societally available energy, imposing unacceptably high energy prices that would induce either fossil resource extraction beyond the safely recoverable resources or energy poverty.