"The Eurogroup answered the call from our citizens for a Europe that protects," Mario Centeno, president of the body representing Eurozone finance ministers, tweeted on Friday morning.
Agreement had been reached on safety nets for workers, businesses and public finances, as well as on a recovery plan.
The emergency rescue package promises to make available more than half a trillion euros to cushion the impact of the coronavirus pandemic across Europe.
The compromise deal is a breakthrough after rival factions had been locked in deadlock: marathon talks earlier in the week broke up in failure.
What are the measures for people and firms?
The deal provides a safety net for healthcare systems overwhelmed by the COVID-19 crisis.
Governments can apply for access -- under certain conditions -- to a total of €240 billion being made available under the European Stability Mechanism (ESM), the bailout fund created during the eurozone debt crisis.
"The only requirement to access the credit line will be that the country would commit to using these funds to support domestic financing of direct and indirect healthcare, cure and prevention related costs due to the COVID 19," Mario Centeno said following the Eurogroup videoconference.
There are also safety nets for workers and the self-employed. An European Commission plan to prevent companies laying off workers, announced last week, is given the go-ahead.
The €100 billion fund called SURE -- to "keep jobs and businesses running" in the words of Commission president Ursula von der Leyen -- involves loans to national governments who would provide guarantees to the EU budget.
Under the safety net for companies, small and medium-sized businesses (SMEs) are to be helped via an EU-wide loan scheme. In addition to creating a €25 billion guarantee fund, the European Investment Bank (EIB) initiative guarantees €200 billion of lending, which should involve national banks. The Eurogroup calls on the EIB to get the scheme up and running as soon as possible.
What else has been done?
The new measures come on top of money channelled by national governments to bolster health and other public services, and support workers and industries. Countries have also pledged to make sure sectors in trouble have access to cash, via public guarantees and deferred tax payments.
Last month the European Central Bank announced a package worth €750 billion to buy up government and company debt across the eurozone.
How soon will schemes be up and running?
The deal has to be signed off by national leaders who will gather for a video conference next week. The Eurogroup statement calls for the plan to be taken up "without delay".
However it's likely that some aspects of the plan will involve further wrangling between governments, EU lawmakers and officials before it can be fully implemented.
It's hoped the €240 billion credit scheme for health systems will be accessible within a fortnight. For companies, the Eurogroup calls on the EIB to get its plan up and running "as soon as possible and stand ready to put it in place without delay".
What isn't addressed by the measures?
The rescue package concerns only short-term economic measures to deal with the immediate impact of the coronavirus pandemic.
But it does not deal with the thorny question of how to pay for the longer-term reconstruction effort in the aftermath. There are big disagreements over how what's called the "EU Recovery Fund" will take shape.
The paragraph in the Eurogroup statement is relatively brief on this matter. It sets out the aims: "providing funding through the EU budget to programmes designed to kick-start the economy".
But exactly how this will be done, not least how to ensure another key goal -- "ensuring EU solidarity with the most affected member states" -- is left to future discussions.
So how united - or disunited - are EU countries?
The agreement is a compromise. On immediate funding for countries in need, the Netherlands backed down on an original demand for reform and oversight.
Instead there are no conditions where the money goes directly or indirectly towards healthcare, and only for the duration of the coronavirus crisis.
"Europe decides and shows it stands up to the gravity of the situation," tweeted French finance minister Bruno Le Maire. His German equivalent Olaf Scholz praised a "big day of European solidarity".
But put off for now is the issue that has created the big fault line between north and south within the EU: whether debt should be shared via "corona bonds".
The idea, which would see debt mutualised by all EU member states, is strongly opposed by the "Frugal Four", led by Germany and the Netherlands. Its backers -- nine countries including France, Italy and Spain -- have agreed to delay a decision.
Euronews correspondent Shona Murray says corona bonds were the "elephant in the room" at the Eurogroup meeting.
"That has been left quite ambiguous in true EU style. It's been kicked up towards the leaders -- the heads of state and government," she told Good Morning Europe.
The agreement mentions the use of "innovative financial instruments" regarding the future Recovery Fund. "The Dutch side has clarified... saying this does not mean corona bonds. The Italian finance minister said last night: 'This means corona bonds are on the table'.
"So, true EU fudgery there," says Murray.
Watch Shona Murray reporting for Good Morning Europe in the video player above.