Regling will head the ESM as it prepares to take on a key role in solving the eurozone debt crisis, offering direct aid to member states.
His nomination was one of several decided by eurozone finance ministers and announced by Eurogroup head and Luxembourg premier Jean-Claude Juncker, including Juncker's own reappointment.
Regling has headed the European Financial Stability Facility (EFSF) since it was set up in the spring of 2010 in the wake of the Greece debt crisis.
The €500-billion-euro ($630-billion) ESM was supposed to begin operations Monday but has been delayed pending ratification by the required number of European states.
Germany's Constitutional Court is expected to begin deciding whether the ESM conforms with the constitution on Tuesday.
The "firewall" is destined to play the role of a "European monetary fund" that offers loans to countries facing financial difficulties on the basis of agreed conditions, or programmes, and which will be able to recapitalise ailing banks directly without adding to the country's national debt.