"Today I'm very happy, because it can be said that Teresa has overcome this illness," Romero's husband, Javier Limon, said in a video statement released by a family spokeswoman.
Two earlier tests showed that Ebola levels in the health worker were almost nil, and a third test came back negative.
"The last two measurements were in 'background' levels, and there is no significant statistical difference with negative results," Luis Enjuanes, an expert on viruses, said in a phone interview, in English, with CNN. "If for three times, throughout one week, you are background, background, background, in practical terms it means you don't have the virus."
Officials have previously said that the amount of the Ebola virus in Romero's blood had decreased dramatically from the time she was rushed to the hospital two weeks ago, but Enjuanes explained just how close to negative she has already come, even before the latest test sample on Sunday.
Romero has recovered enough to produce antibodies, he said.
"It means she's making her own protection, so any virus fooling around probably will be destroyed or neutralized," said Enjuanes, who's been attending the near-daily meetings of the government's special committee on Ebola, a panel of medical and scientific experts convened to deal with the crisis.
Even though Romero received the negative result for the Ebola virus on this third key test in a week, she will surely remain in hospital for days, possibly a few weeks, in order to recover, Enjuanes said.
She has received two main treatments in her battle against Ebola, for which there is still no vaccine. The first was an IV drip with the antibodies of an Ebola survivor -- a Catholic nun who survived the disease in West Africa. And Romero also received an experimental anti-viral drug, favipiravir, Enjuanes said.
Spain imported another experimental drug, ZMab, but could only get an older version -- not the newest version, whose stocks have run low globally -- and Romero's doctors decided not to use it on her, Enjuanes said.
To fight her lung problems while also battling Ebola, the doctors administered anti-inflammatory drugs to ease her respiratory problems, even while unsure how that treatment might affect the anti-Ebola measures, Enjuanes said.
Other patients test negative
Two other patients being monitored at Carlos III hospital also tested negative for the virus on Sunday, according to the Special Ebola Committee.
The National Microbiology Institute received tests of Romero and the two other individuals under observation at Carlos III hospital, said the institute's director, Manuel Cuenca.
The tests from a man under observation in Tenerife will be received on Monday, Cuenca told CNN.
As of Sunday morning, Ramos was the only confirmed Ebola patient, according to a statement from the committee.