The amount is broadly in line with market expectations of 60bn euros, and follows so-called stress tests of 14 Spanish lenders.
Much of the money is expected to come from the eurozone rescue funds, the current EFSF and the future ESM.
Spain said in July that it would request eurozone support for its banks.
The Spanish banking sector has been in difficulty since the global financial crisis of 2008, and the subsequent bursting of the country's property bubble and deep recession.
The European Commission welcomed the announcement, saying in a statement that it "is a major step in implementing the financial-assistance programme and towards strengthening the viability of, and confidence in, the Spanish banking sector".
It added: "The necessary state aid provided to Spanish banks will be determined in the coming months."
The Commission also said that it expected the first Spanish banks to start recieving the loans "by November."
By Laurence KnightBusiness reporter, BBC News
An independent audit of the banks confirmed on Friday that the banks are short of some 59bn euros, or almost 6% of Spanish GDP.
This "hole" is the amount of capital that must be injected by the authorities to absorb the losses that the banks (especially regional savings banks) might suffer on all the loans they made to property developers and mortgage borrowers during the housing boom of the last decade.
Some of the 59bn may also be provided by private sector investors, or by writing off the amount owed to some existing investors in the banks.
The housing bubble has burst and many of those loans cannot be repaid.
The eurozone has already made 100bn euros available from its rescue funds to plug this hole, although many investors suspect that the banks' needs may (eventually) exceed even this total.
For Spain, the question isn't just the size of the banks' losses.
It is still not clear who will ultimately bear them. Will it be the entire eurozone, through its 100bn-euro investment (as Madrid hopes), the Spanish government itself, or the (mostly Spanish) private sector investors in the banks?
The Irish government was sunk by the losses incurred by its own banks after it foolishly offered to guarantee them. Spain hopes to avoid the same fate.
Six burning questions for Spain
Christine Lagarde, managing director of the International Monetary Fund, praised the independent valuation of Spain's banks, saying it had been "thorough and transparent".
She added: "Public funding of the banks' actual capital needs, which are expected to be lower than the amounts identified in the stress tests, can be financed comfortably under the recapitalisation programme supported by Spain's European partners."
The audit calculation that Spain's banks will need 59.3bn euros is a worst-case scenario, and does not take into account any future plans by the lenders themselves to raise their own capital.
The country's economy minister Fernando Jimenez  Latorre indicated that it may need to borrow about 40bn from the eurozone rescue funds.
Bankia was found to be the bank most in need of additional capital, requiring 24.7bn euros. It was followed by Catalunya Bank (10.8bn euros), Novagalicia (7.2bn euros), Banco de Valencia (3.5bn euros), Banco Popular (3.2bn euros), Banco Mare Nostrum (2.2bn euros), and Ibercaja-Liberbank-Caja (2.1bn euros).
Seven Spanish banks have no need for extra capital - Santander, BBVA, Caixabank, Kutxabank, Sabadell, Bankinter, and Unicaja.
The audit was also based on a number of assumptions, including that Spain's economy will contract by 6.5% between 2012 and 2014.
The Open Europe think tank suggested many of these were overly optimistic, however.
"These tests do look to be more intense than the previous ones but ultimately the optimistic assumptions do instantly raise questions over their credibility," the group said.
"The prediction that unemployment will peak at 27.2% seems optimistic given that there is plenty more austerity and internal devaluation to come while the structural labour market reforms are yet to take effect."
It added that a worsening economic situation would also increase the number of loans which are defaulted on and hit the value of the foreclosed properties which banks own.
The bigger question remains whether the Spanish government will have to follow Greece, Portugal and the Republic of Ireland and request a full international bailout, involving loans that have to be paid off by the state, as well as close monitoring of its economy by its international creditors.
While Madrid continues to publicly deny this, the markets consider it only a matter of time.
On Thursday, the Spanish government announced its latest austerity budget. Against a backdrop of violent protests, it outlined new spending cuts, but protected pensions.
Spain is struggling with a shrinking economy and 25% unemployment.
Comments from its central bank earlier this week indicated that the country's recession deepened in the past three months.
As tax revenues fall and benefits payments rise in a recession, this will make it even harder for Spain to get its finances under control.
Spain's banks will need an injection of 59.3bn euros ($76.3bn; £47.3bn) to survive a serious downturn, an independent audit has calculated.