Alireza Jamshidi, an Iranian judiciary spokesman, told the official IRNA news agency: "In consideration of this ruling, naturally she will be freed."
Saberi's father, Reza, said he had been told his daughter would be freed soon.
"We are waiting in front of the prison for her to come out so we can take her home," he said.
"She was very hopeful and we were very hopeful [that she would win the appeal], so we are happy with the news."
The ruling came after a court in the capital, Tehran, heard Saberi's appeal behind closed doors.
"We couldn’t believe it [when Roxanna was convicted]. Roxanna is a balanced reporter. She never took sides.
"She never intended to pass any news to any other country that was against the interest of Iran. She hasn’t done anything wrong.
"Whatever happened in the courts we don’t know. We are happy they have decided to release her.
"I need to talk to my daughter to find out what the real scenario was, why they arrested her and why they kept her.
"There will be some friends around to celebrate but tonight of course we just want her to rest, when we go home we will celebrate."
Saberi was initially detained in January reportedly for buying alcohol, but was later charged with espionage.
"The article of law that was referred to in her conviction was article 501 that says any co-operation with hostile governments and hostile countries deserved one to 10 years in prison," Al Jazeera's Alireza Ronaghi, reporting fom Tehran, said.
"That article of law has been disputed by lawyers who say Iran is not at war with anyone at the moment and the phrase of 'hostile government' should be interpreted more seriously."
Saberi has reported for US National Public Radio, the BBC and Fox News, and has lived in Iran for the past six years. Tehran says that she has been working in the country illegally after her press card was revoked in 2006.
The original sentence was handed down just weeks after Barack Obama, the US president, said that his administration would work towards better relations with Tehran after three decades of with no official ties.
Al Jazeera's Ronaghi said: "They [Iran] don't want to jeopardise all the possibilities and potential of future changes in Iran-US relations with one court order."
Washington has repeatedly denied that Saberi was involved in spying for the US.