Cwele did not speak to waiting journalists.
Smartly dressed in black dress and wearing a black and white floral coat, Cwele entered the building. She was expected to be taken to Durban's Westville Prison in a police van later.
Cwele and her co-accused Frank Nabolisa failed to have their convictions overturned by the Supreme Court of Appeal on Monday. The court also increased their sentences from 12 to 20 years.
Court president Lex Mpati said the sentence imposed by the trial court was disturbingly inappropriate.
Cwele (50) was only appealing her conviction, while Nabolisa appealed both his conviction and sentence.
Cwele was given three days upon receipt of the judgment to hand herself to authorities.
The National Prosecuting Authority said the two could still launch an appeal with the Constitutional Court.
"[They] have 21 days to hand an application in at the ConCourt," said NPA spokesperson Natasha Ramkisoon.
"But there was no indication of any constitutional grounds mentioned of this at the case," she added.
Both pleaded not guilty to conspiring to deal in drugs, to procuring a woman, Charmaine Moss, to collect drugs in Turkey, and to procuring another woman, Tessa Beetge, to smuggle cocaine from South America.
The two were found guilty of drug dealing by the Pietermaritzburg High Court in May 2011.
Nabolisa had been in custody until now. Cwele was out on R100 000 bail. She is the ex-wife of State Security Minister Siyabonga Cwele. – Sapa