Teresa Romero, who was hospitalized in Madrid on October 6, will have to undergo a second test before she can be declared free of the deadly virus, the Spanish government said.
Romero, 44, contracted the tropical fever after caring for two Ebola patients who died at Madrid's Carlos III hospital, in the first known case of transmission outside Africa.
She will be given another test "in the coming hours", according to a statement from Spain's special Ebola committee, which added that her "health was... developing favourably".
"I am very happy today because we can say Teresa beat the disease," Romero's husband Javier Limon said in a video filmed at the hospital where he is being kept under observation with 14 other people who had contact with Romero before she was diagnosed.
The worst-ever outbreak of the deadly virus has so far killed more than 4,500 people, almost all in west Africa, with close to 2,500 deaths registered in worst-hit Liberia.
Isolated cases among health workers in the US and Europe have sparked fear that the epidemic could turn global and prompted Western countries to ramp up their response.
Liberian President Nobel laureate Ellen Johnson Sirleaf said a generation of Africans were at risk of "being lost to economic catastrophe" because of the crisis, warning that the "time for talking or theorising is over".
"This fight requires a commitment from every nation that has the capacity to help, whether that is with emergency funds, medical supplies or clinical expertise," she said in an open letter to the world published by the BBC Sunday.
The deadly virus, for which there is currently no licensed treatment or vaccine, spreads via contact with bodily fluids.
Some countries have managed to get a handle on the outbreak, with Africa's most populous nation Nigeria expected to be declared free of the deadly virus on Monday after 42 days without registering any new infections.
Also on Monday, European Union foreign ministers will meet in Luxembourg to try and devise a new strategy to combat the outbreak, including by freeing up more funds and sending skilled staff to Africa.
Ahead of the talks, German Foreign Minister Frank-Walter Steinmeier said the bloc should consider sending "a civilian EU mission" to west Africa.
"This would offer a platform to (EU) member states" to send medical staff to the region, he said at a health forum in Berlin.
One EU diplomat said Britain, which already has a navy ship bound for Sierra Leone laden with medical staff and supplies, hoped to "galvanise EU action on Ebola".
"There is a real sense that this is a tipping point and we must get to grips with it now," said the diplomat. "If we can deal with it in the country, we don't have to deal with it at home."
Another diplomat said there are plans for three nations to spearhead global aid to the worst-hit countries: the United States for Liberia, Britain for Sierra Leone and France for Guinea.
A global UN appeal for nearly $1 billion (785 billion euros) has so far fallen short, with only $385.9 million given by governments and agencies, with a further $225.8 million promised.
'We made mistakes'
With panic spreading in western countries about the tropical disease, US President Barack Obama on Saturday cautioned Americans against "hysteria".
US media have been reporting on a string of false alarms among a public spooked by the news that two American nurses at a Texas hospital had contracted the virus after treating a Liberian patient who died from Ebola on October 8.
The Texas Health Presbyterian Hospital on Sunday apologised over its handling of the case.
"As an institution, we made mistakes in handling this very difficult challenge," the hospital said in a "letter to our community" that was published in Sunday's Dallas Morning News.
The United States, Britain and Canada were joined by France this weekend in screening air passengers from Ebola-hit zones ahead of a review of EU practices this week.
Belgium's prime minister said it would start screening passengers from west Africa on Monday, while France dismissed a call by unions representing Air France cabin staff to suspend flights to Guinea.
French foreign minister Laurent Fabius, speaking during a visit to Beijing, warned that halting the airline's daily Paris-Conakry flight would encourage riskier forms of travel that could spread the virus even faster.
Obama has also played down the idea of a travel ban on flights from west Africa.
As of October 14, 4,555 people had died from Ebola out of a total of 9,216 cases registered in seven countries, the Geneva-based World Health Organization said.
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