The fund will be created from contributions from all the participating banks under the scheme and is aiming to reach 55 billion euros in eight years.
"The banking union really is the cornerstone because everybody has understood the stability or instability of the euro zone relates to the stability of the whole of the single market and we are all responsible for that," Michel Barnier, the EU's market chief said in Parliament.
Read MoreEurope's new banking union: Why you should care
"We need to make sure the financial sector is there to serve the real economy rather than serve themselves which we have seen too much in the last 30 years."
Banking union 'failure'
The SRM will come in to effect from January 1 2015, while the process for bail-in and resolution for failed banks will begin in 2016.
Members of the European Parliament, the European Commission and national finance ministers locked horns in a marathon 16-hour meeting last month to nail down the details of this bill. While a compromise was reached, some lawmakers still thought the legislation was limited.
Portuguese Communist MEP Marisa Matias called the banking union the best example of "failure to keep promises" and dubbed the ECB "the most powerful undemocratic institution in the world".
Read MoreEurope banks get downgrade warning amid 'bail-in' concerns
British UKIP MEP Roger Helmer claimed the proposals were "inadequate" and slammed the euro as "the underlying cancer".
Coordinating cross border efforts on monitoring the banking sector will be difficult and the success of the latest raft of measures depends on whether authorities across the European Union work together, according to one lawyer.
"Whilst the takeover of the bank's control and the bank's resolution are only seen as last resorts, by setting out common rules the aim is to facilitate cross-border resolutions. But how well this works in practice will be down to how the European and national supervisors and resolution authorities across the EU work together," David Ereira, partner at Linklaters, said in an emailed statement.