A spokeswoman for the Norwegian foreign ministry said that Dalelv had been pardoned by Dubai ruler Sheikh Mohammed bin Rashid al-Maktoum.
"She hasn't been deported, she has been pardoned. She can remain in Dubai if she wishes. Her passport has been returned to her," foreign ministry spokeswoman Ragnhild Imerslund said.
"She will travel home shortly," she added.
Dalelv, 24, risked 16 months in jail after being convicted last week by a Dubai court of extramarital sex, perjury and consuming alcohol without a licence.
She was detained when reporting being raped to police in the United Arab Emirates in March, 2013.
Dalelv was released four days later with the assistance of Norwegian diplomats and has been staying at the Norwegian Seamen's Church in Dubai for the past several months.
"I am very nervous and tense. But I hope for the best and I take one day at a time. I just have to get through this," she said on Friday.