Sweden Finance Minister Anders Borg has reportedly told the news agency Ritzau that he is happy with the agreement, which was voted through in the early hours of Thursday after 14 hours at the negotiating table.
The Financial Times newspaper called it Europe’s “first big step towards a banking union”.
Germany and France had a few kinks to iron out, reportedly taking up four of the 14 hours spent discussing.
The common currency members vis-à-vis their non-eurozone neighbours also had several issues that needed dealing with, the German Finance Minister Wolfgang Schäuble told Ritzau.
The 17 eurozone countries will be bound to the agreement, while Sweden has a respite period before giving its final decision on whether to partake or not.
The FT reports that Sweden and the UK were among the most vocal critics of extending the power of the European Central Bank too far into national banking territory.
The regulations should come into force March 1st, 2014 and will be overseen by a regulator based in Frankfurt.