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It said the measure had been finalised in a cabinet meeting on Monday.
Foreign Minister Arancha Gonzalez Laya had previously said the requirement would be lifted in July, without giving a date.
The news comes as the UK government prepares to bring in its own 14-day quarantine policy from 8 June.
Travel firms and other industry bodies say the UK should relax the measure for visitors arriving from countries where people are at a lower risk of contracting the coronavirus.
Spain normally attracts 80 million tourists a year, with the sector providing more than 12% of the country's GDP.
Opening up the holiday market again before the summer season is over is seen as crucial to the Spanish economy.
But under the UK's new policy, any tourists returning home after taking holidays in Spain and most other foreign destinations would have to spend two weeks in self-isolation.
Resuming flights
Several airlines including EasyJet, Jet2 and Ryanair have announced that they plan to resume flights and holidays soon.
Easyjet will be resuming flights from 22 airports across Europe from 15 June, as well as regional flights across the UK. But there will only be one international flight from the UK - from Gatwick to Nice in France.
Jet2 is planning to resume full services from 1 July, and will fly to several Spanish and Italian destinations, before opening up to Greece and Croatia later in the year.
And Ryanair will be restoring 40% of its flights from 1 July and will resume flights from most of the 80 airports it flies from across Europe.
Business groups wrote to Boris Johnson on Sunday saying the quarantine would have "serious consequences" for the economy and calling for "air bridge" deals to be struck with other nations.
In their letter to the prime minister, bosses of airlines EasyJet, Tui, Jet2 and Virgin Atlantic, as well as industry bodies Airlines UK, the British Chambers of Commerce, UK Hospitality and manufacturing association Made UK said they had "serious reservations" about a "blanket approach" to all arrivals into Britain.
Instead, they are asking for a more "targeted, risk-based" approach when establishing air links with countries that have high infection rates from the pandemic.
"The alternative risks major damage to the arteries of UK trade with key industry supply chains, whilst pushing the UK to the back of the queue as states begin conversations for opening up their borders," says the letter. BBC