Council of the European Union:

The Eurogroup is an informal body where the ministers of the euro area member states discuss matters relating to their shared responsibilities related to the euro.

Protocol 14 to the Treaty on the Functioning of the European Union [PDF]

ON THE EURO GROUP

THE HIGH CONTRACTING PARTIES,

DESIRING to promote conditions for stronger economic growth in the European Union and, to that end, to develop ever closer coordination of economic policies within the euro area,

CONSCIOUS of the need to lay down special provisions for enhanced dialogue between the Member States whose currency is the euro, pending the euro becoming the currency of all Member States of the Union,

HAVE AGREED UPON the following provisions, which shall be annexed to the Treaty on European Union and to the Treaty on the Functioning of the European Union:

Article 1

The Ministers of the Member States whose currency is the euro shall meet informally. Such meetings shall take place, when necessary, to discuss questions related to the specific responsibilities they share with regard to the single currency. The Commission shall take part in the meetings. The European Central Bank shall be invited to take part in such meetings, which shall be prepared by the representatives of the Ministers with responsibility for finance of the Member States whose currency is the euro and of the Commission.

Article 2

The Ministers of the Member States whose currency is the euro shall elect a president for two and a half years, by a majority of those Member States.

Why there was a need to attach a protocol to the Treaties for this purpose, I do not know.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman