Ayaan Hirsi Ali, a fierce critic of radical Islam, resigned from parliament in May and said she would leave the country after Rita Verdonk, the Dutch immigration minister and a member of her own VVD liberal party, told her she could lose her citizenship.
However, Dutch cabinet members agreed late on Monday that Hirsi Ali, whose real name is Hirsi Magan, should not be stripped of her citizenship. Verdonk told parliament on Tuesday that Hirsi Ali would be able to keep her Dutch nationality.
Verdonk added in a statement that her initial decision to strip Hirsi Ali of Dutch citizenship was not based on a full understanding of the circumstances of her name change.
Hirsi Ali hit the headllines in 2004 after the Dutch filmmaker Theo Van Gogh, who directed a film she wrote which accused Islam of suppressing women, was murdered by a Muslim extremist.
Hirsi Ali, 36, had admitted using a false name and date of birth when she arrived in the Netherlands in 1992.
Dutch cabinet members agreed that because she used her grandfather's name, which is allowed under Somali law, the false claim would not be held against her.
In a published statement, Hirsi Ali said that she would continue to use Hirsi Ali as her name and regretted giving authorities the wrong impression about her identity.
Verdonk said her initial decision
was not based on full information
Her lawyer also said she was "happy the uncertainty is finally over [and that] there are no more questions about her Dutch citizenship".
On her asylum application Hirsi Ali also pretended she had come to the Netherlands from Somalia, rather than via Kenya and Germany.
Refugees are usually required to apply for asylum in the first safe country they reach after fleeing.
However, she said those facts had been public knowledge when the VVD chose her as a candidate for parliament in 2002.
Hirsi Ali went into hiding in 2004 after Van Gogh's death. His murderer, Mohammed Bouyeri, is currently serving life in prison.
Hirsi Ali returned to parliament a few months after the murder but has continued to live under heavy guard.
She has since been offered a job by the American Enterprise Institute, a conservative think-tank in the US capital, Washington DC.