After 13 hours of talks, they also agreed to set up a joint banking supervisory body for the eurozone.
Spain and Italy put pressure on Germany to allow the bailout fund to buy government debt in the markets - a measure to contain borrowing costs.
Eurozone leaders agreed to begin implementing the decisions by 9 July.
However, it could take until the end of the year before the new money becomes available.
Announcing the deal, EU Council President Herman van Rompuy said it would break the "vicious circle" between banks and national governments.
The euro surged against the dollar in Asian trade after the news from Brussels. Stocks in Germany and London also rose sharply.
The deal also tried to sort out a problem with a previous agreement to lend money to Spain's banks. There had been confusion over where that money would come from, and which lenders would have priority in the event of a default.
The new agreement made clear that the EU's existing bailout fund will provide aid under the current rules until the new fund, the European Stabilisation Mechanism (ESM), begins operations.
The BBC's Andrew Walker, in Brussels, says these loans will also not be given "seniority" over private sector loans.
This means that if Spain were to default, those official lenders would not get preferential treatment. The move should make Spanish government debt a little more attractive to private investors, our correspondent says.
Analysts say Germany appears to have given ground after pressure from Spain and Italy to provide more support.
The two southern European countries had withheld support from an earlier plan for a growth package worth 120bn euros (£96bn; $149bn).
They wanted measures to lower their borrowing costs.
Our corresopndent says although Germany appears to have compromised, Chancellor Angela Merkel has managed to ensure that Brussels has more control over the finances of eurozone countries, something she had wanted.
The deal came about after new French President Francois Hollande appeared to throw his weight behind Italy and Spain.
"I'm here to try to find rapid solutions for those countries facing pressure from the market, despite having made huge efforts to balance their budgets," the socialist French president said.
The new growth package, announced by Mr Rompuy, is made up of:
A 10bn-euro boost of capital for the European Investment Bank, expected to raise overall lending capacity by 60bn euros
Targeting 60bn euros of unused structural funds to help small enterprises and create youth employment
A pilot launch of EU project bonds worth 4.5bn euros for infrastructure improvements, focusing on energy, transport and broadband.
'No magic formula'
In Brussels, both Italy and Spain were pushing the eurozone bloc to agree steps to reduce the interest rates the two countries have to pay.
Spanish 10-year government bonds were trading at yields above 6.9% on Thursday, coming close to the 7% considered unaffordable.
Spain's Prime Minister Mariano Rajoy said debt sustainability was a pressing problem.
"We are paying rates that are too high to finance ourselves and there are many Spanish public institutions that cannot finance themselves."
Spanish and Italian leaders are worried that their countries could soon - in effect - be shut out of international markets and forced to seek assistance.
Mrs Merkel has warned there is no "magic formula" to solve the crisis.
Several EU leaders want individual countries' debts guaranteed by the whole eurozone, for instance in the form of centrally issued eurobonds.
But Mrs Merkel told the German parliament on Wednesday that eurobonds were "the wrong way" and "counter-productive", adding: "We are working to breach the vicious circle of piling up debt and breaking [EU] rules."
She said to loud applause: "Joint liability can only happen when sufficient controls are in place."
Stronger competitiveness was the condition for sustained growth, the chancellor said.
Meanwhile, UK Prime Minister David Cameron said on his arrival at the summit that eurozone countries had some "hard decisions" to make.
When asked about plans for transferring more budgetary powers to the EU level, he said he shared "people's concerns about Brussels getting too much power".
European authorities have also unveiled proposals such as the creation of a European treasury, which would have powers over national budgets. The 10-year plan is designed to strengthen the eurozone and prevent future crises, but critics say it will not address current debt problems.