Last month, Armstrong was convicted of trying to smuggle cocaine after being duped in a sophisticated internet honeytrap sting.
A judge accepted she had no clue the drugs were in her suitcase - but that was not enough for her to be cleared.
Armstrong has spent nearly a year in an Argentinian jail and will be eligible for parole in late 2013. In a statement, her family said they would appeal against the verdict.
Armstrong was stopped at Ezeiza International Airport with 5kg of cocaine in her suitcase last April.
The former Maori Language Commission boss arranged to fly to London to meet a man after months of online exchanges - she agreed to fly via Argentina to pick up some "paperwork" for him.
Her mystery boyfriend, believed to be an African man who had claimed to live in London, and alleged accomplices have not been found. Argentinian media reported Armstrong's lawyer produced evidence at her trial of South American gangs specialising in love stings.
The family statement said: "Since receiving the decision the family has taken some private time to deal with the outcome and decide whether to proceed with an appeal.
"Following consultation with their Argentinian legal team, which confirmed their belief that the decision should be appealed, they have decided to fund an appeal against conviction.
"The family are resolute in their belief that Sharon is not guilty; they accept she made a foolish error in agreeing to carry the suitcase which was later found to have cocaine concealed inside but they know that she would not become involved in any form of criminal drug activity."