A three-region optimal economic growth model is proposed to represent the global energy transition to net-zero emissions when carbon dioxide removal (CDR) technologies are available. The main features of the model are (i) the representation of the economy and energy use with nested CES production functions; (ii) the representation of climate policy through the use of a safety cumulative emissions budget concept; and (iii) the introduction of an international emissions trading scheme for the implementation of climate policy. Using an infinite horizon optimal control paradigm, several contrasting scenarios are analyzed both in an asymptotic steady state or "turnpike" point, and in an optimal transition to sustainability. This very compact model produces dynamic path simulations that are consistent with the main recommendations from IPCC for long term climate policies. The potential use of this simple model in future developments in climate and economic modeling is discussed.