Ms Hirsi Ali told a press conference she would resign immediately and leave the Netherlands.
"Today I resign as a member of parliament. I will leave the Netherlands, saddened but also relieved," she said.
A fierce critic of conservative Islam, Ms Hirsi Ali rose to prominence in 2004 when her friend and colleague Theo Van Gogh was murdered by a Muslim extremist, angered by his TV film Submission, which was written by Ms Hirsi Ali.
She has since received death threats and had to be under police protection.
Her resignation comes after Immigration Minister Rita Verdonk, who is a member of Ms Hirsi Ali's centre-right-wing VVD party, told parliament that the Somali-born MP's citizenship was being revoked because she had provided false information on her asylum application.
A Dutch television program last week broadcast details of her falsified asylum application, in which she admitted to claiming to have come to the Netherlands directly from Somalia, when in fact she had lived in three different countries in the interim.
She also used a false name and date of birth when she arrived, to stop her family finding her after she fled an arranged marriage with a cousin in Canada.
But she said she already admitted lying to win asylum when she was vetted as a parliamentary candidate in 2002.
Ms Verdonk said that because of the false information, the application and her Dutch citizenship are invalid.
Ms Hirsi Ali said she was "extremely disappointed" and "astonished" that her citizenship would most likely be stripped.
The immigration minister's decision sparked a storm of criticism even from within the VU, and parliament called an emergency debate on the matter for Wednesday, where the minister will answer questions.
Ms Hirsi Ali said she had decided to move abroad before the controversy about her asylum application arose because a Dutch court had ordered her to move out of her government-secured house after complaints from her neighbours.
"It is difficult to live with so many threats on your life and such a level of police protection," Hirsi Ali was quoted by the Associated Press news agency as saying.
Dutch media has reported that she will go to the US and work for a conservative think tank in Washington.