She now faces losing her Dutch passport.
Hirsi Ali said she had made the decision on Monday night, after Rita Verdonk, the immigration minister, told her she would be stripped of her Dutch citizenship.
"I am therefore preparing to leave Holland," Hirsi Ali said at a press conference in the Hague on Tuesday.
Hirsi Ali, 36, falsified her name and date of birth on her asylum application when she arrived in 1992, fearing reprisals from her family after she claimed she fled from an arranged marriage.
She was granted a passport in 1997 and acknowledged the falsification in 2002 during vetting as a candidate for parliament. There were no objections at the time.
But after a Dutch television programme re-aired the matter last week, Verdonk ruled her naturalisation had been improperly granted.
The documentary screened interviews with members of her family who said she had not been forced into an arranged marriage and had had nothing to fear.
Asked whether she had falsified her asylum application, Hirsi Ali told the programme she lied about her name, age and how she came to the Netherlands.
Dutch vice-prime minister Gerrit Zalm, who was the leader of Hirsi Ali's VVD party in 2002, spoke at the same news conference and said he was "amazed at the speed" with which Verdonk's decision was made.
After Theo Van Gogh's murder,
Hirsi Ali went into hiding
"If she reapplies for citizenship, I trust her application will be handled with the same urgency," he said.
Hirsi Ali became internationally known after the murder of filmmaker Theo van Gogh in November 2004. She wrote the script for Van Gogh's film Submission, which accuses Islam of suppressing women.
She went into hiding for several months after Van Gogh's killing and has lived under heavy guard ever since.
The Dutch state had been scrambling to arrange new housing for her after her neighbours in The Hague complained successfully last month that security arrangements for her had become an unbearable nuisance for them.
A court ruled she must leave her home by August.
"It is difficult to work as a parliamentarian if you have nowhere to live. All that is difficult but not impossible. It has become impossible since last night," said Hirsi Ali, whose real name is Hirsi Magan.
She 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.
Dutch media reported on Monday that Hirsi Ali had obtained a post at the American Enterprise Institute, a right-wing think-tank which has provided members of US President George W Bush's administration.
Hirsi Ali's popularity has slipped of late.
A poll showed that only 25% saw her departure as a loss for Dutch politics.