"I was told that I've been pardoned," Marte Deborah Dalelv said adding that her passport had been returned and she would leave the Gulf state "as soon as possible".
"I'm very, very happy. This is the perfect ending (and) it feels really, really good," a smiling Dalelv told reporters.
Qatar-based interior designer Dalelv, dressed in a white shirt and a mid-length skirt, informed about the end of four-month ordeal outside a Scandinavian social centre.
The minister wrote on Twitter that she would be returning home soon.
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Eide has said it was "very strange that a person who reports rape is sentenced for acts which in our part of the world is not even a crime."
Dalelv was on a business trip to Dubai in March when she alleged she was raped by a colleague at the hotel where she was staying.
She reported the attack to police, but found herself detained and charged with having unlawful sex, making a false statement and illegal consumption of alcohol. Her passport was confiscated and her money seized by police.
A court last week sentenced Dalelv to 16 months in prison, while her alleged attacker received a 13-month sentence for extra-marital sex and alcohol consumption.
Her alleged attacker has also been pardoned, a Norwegian official said.
The alleged attacker, a Sudanese identified as Hawari in his 30s, "was also handed back his passport" and freed, Dalelv's lawyer Azab told reporters.
Amid a global outcry from rights groups demanding her release, Dubai's ruler Sheikh Mohammed bin Rashid Al Maktoum pardoned Dalelv.
Dalelv has been staying at the Norwegian Seamen's Church in Dubai since March.