The mother and sister of Michaella McCollum, 20, from Dungannon, Co Tyrone, also vowed to mount a legal bid to get her to serve her sentence in a Northern Ireland jail.
McCollum along with co-accused Melissa Reid, 20, from Lenzie near Glasgow, pled guilty to drug smuggling in September.
They had faced the prospect of a maximum 15-year prison term but struck a behind-closed-doors plea bargain to secure a shorter sentence.
On Tuesday, they were sentenced to six years and eight months in prison, the shortest sentence they could have received.
McCollum's sister Samantha said:"In our opinion she will always be innocent."
"Michaella has never been in trouble before. We will all support her."
McCollum's mother Nora, who described her daughter as an "honest, hard-working girl", said she was "optimistic" after hearing the length of sentence.
Before pleading guilty, both women said Colombian drug lords kidnapped them and forced them to board a flight from Lima to Spain in August with 24lb of cocaine in food packets.
So far they have been held at the notorious Virgen de Fatima prison in Lima.