King Buyelekhaya Dalindyebo was convicted of kidnapping, assault and arson.
He has been ordered to report to police within 48 hours or risk arrest, sources close to the king have told the BBC.
King Dalindyebo comes from the Thembu ethnic group, to which anti-apartheid icon Nelson Mandela belonged.
He is the first monarch to be given a jail term since South Africa became a democracy in 1994.
The case was related to a dispute King Dalindyebo had with some of his subjects more than two decades ago.
He was accused of kidnapping a woman and her six children, setting their home on fire and beating up four youths, one of whom died, because one of their relatives had failed to present himself before the kings’s traditional court.
The Constitutional Court refused to hear the case, meaning that he has run out of legal options and the ruling of the Supreme Court of Appeal stands, the BBC’s Pumza Fihlani in Johannesburg says.
“His behaviour was all the more deplorable because the victims of his reign of terror were the vulnerable rural poor, who were dependent upon him. Our constitution does not countenance such behaviour,” the Supreme Court of Appeal said in a judgement in October.
“We are a constitutional democracy in which everyone is accountable and where the most vulnerable are entitled to protection,” it added.
Our correspondent says many people feel King Dalindyebo has disgraced the royal family, and he will be hard-pressed to find any sympathy.
There is already talk of his son Prince Azenethi Dalindyebo being crowned as the next monarch, she adds.
Royal family spokesman Daludumo Mtirara said the decision of the Constitutional Court marked the end of the king’s legal battles, and he had “failed to clear his name in our courts”, the privately owned eNCA news site reports.