Germany's cabinet has approved its contribution to the eurozone and IMF bail-out of Greece.
The German parliament is set to pass the legislation later this week to allow its loan - worth 22.4bn euros (£19.4bn; $29.6bn) over three years - to be paid.
There has been significant public opposition in Germany to assisting the debt-ridden Greek economy.
Markets gave the bail-out deal, agreed over the weekend, a muted response.
Cut ability questioned
Germany was ultimately pushed into action by its own economic interest, with Chancellor Angela Merkel saying the bail-out was "the only way to ensure the stability of the euro".
"The reason for this law is a last resort - an emergency situation - in that Greece in effect no longer had access to the financial markets, and there was an impact on the stability of the euro," Mrs Merkel told a press conference.
She later told ZDF television: "We said time and again, if the stability of our currency was in danger, we would act quickly and decisively. And this is the point that we've reached."
Germany is paying the largest share of the unprecedented 110bn euros rescue package.
But investors have questioned whether the rescue package will be enough to solve Greece's deep-seated problems and whether it will be able to carry out the severe budget cuts agreed as part of the deal.
The first part of the loan will be released before 19 May - the date of Greece's next debt repayment, the EU said.
The IMF is expected to approve its portion of the loan this week, its managing director Dominique Strauss-Kahn said.
Meanwhile, also on Monday French politicians prepared to vote on 16.8bn euros of financial aid for Greece, France's share of the eurozone bailout.
The National Assembly, the lower house of parliament, began debating the measure and were set to vote on it late on Monday evening or on Tuesday.
It must then pass to the Senate later in the week.
Despite the bail-out being approved on Sunday, the euro fell on Monday and European stocks were muted.
The "catastrophe" of Greece defaulting on its debts had been averted by the bail-out said Philippe Gijsels, head of research at BNP Paribas Fortis Global Markets in Brussels.
"But the market realises that it will be a very long, difficult road to travel before it can get better."
Some have also raised doubts about whether Greece will be able to implement the swingeing budget cuts it has promised.
Greece's government will present its bailout package to parliament on Tuesday - with the aim of using emergency rules to get it approved within a week
The cost of the bail-out could have been considerably less had the eurozone nations acted more quickly said Italy's foreign minister Franco Frattini.
"It was necessary to intervene right away to help Greece. To avoid damage we initially talked about 50 billion euros, but decided on 110 billion only 10 days later," he said.
"We respected the prudence of a large country like Germany, we gave it time to think, but during this period the damage has grown."
Meanwhile Luxembourg Prime Minister Jean-Claude Juncker admitted he "almost lost patience" at the slow pace of the bail-out being agreed.
Other senior politicians said the scale of the rescue highlighted the need for stricter public finance controls.
"When it ends up costing you 110 billion euros, you do change your approach," said Christine Lagarde, the finance minister of France which is set to make a 16.8bn euros contribution.
She told Le Monde newspaper early warning systems needed to be put in place to prevent a repeat of the Greek crisis, and that new criteria were needed to monitor the eurozone's 16 members.
Greek shares opened sharply higher before falling back. Meanwhile key German and French indexes were little changed.
Paris's Cac 40 index and Frankfurt's Dax 30 ended the day ahead by 0.30% and 0.51% respectively having traded lower for much of the day. London's stock market was closed for the May Day public holiday.
German government 10-year bonds made slight gains as investors looked for safe investments.
Greek government debt, which was downgraded to junk status last week, fell further - a sign of falling confidence in the Greek economy.
However the European Central Bank extended its lifeline to Greece - saying that Greek government-backed assets such as bonds could still be used to secure funding from the ECB - even if they were not deemed credit-worthy by the ratings agencies.
On Monday, Greece said about 10bn euros of the rescue plan will go towards supporting its banks.
The country is expected to be in recession for three years which will reduce demand for lending and other services on which banks make money.
In return for the financial support, the Greek government has unveiled a fresh round of sweeping efficiencies, including further tax rises and deeper cuts in pensions and public service pay.