Sir Mark Thatcher is thought to be heading to the US after pleading guilty to involvement in an alleged coup plot in the African state Equatorial Guinea.
Thatcher left Cape Town on Thursday to rejoin his family
He left Cape Town on Thursday, but his exact destination was unknown, although he did not travel to London.
He was fined the equivalent of US$500,000 (£265,000) and given a four-year suspended jail term.
Thatcher, who denies any knowledge of the plot, agreed a plea bargain and will now co-operate with investigators.
It is the first time in five months he has been able to leave South Africa, where he had to report daily to police as part of his bail conditions.
Family spokesman Lord Bell said: "He is not in London and he has no current plans to come to London
"As you would imagine, he is anxious to be reunited with his wife and children as soon as possible."
Thatcher, 51, is expected to join his American wife Diane and Michael, 15, and Amanda, 11, in Dallas, Texas.
He admitted breaking anti-mercenary legislation in South Africa by agreeing to finance a helicopter.
The businessman said he did not initially know the helicopter's alleged purpose - that it was to be used in the alleged coup attempt, instead believing it was to be used as an air ambulance.
But in his plea bargain statement, Sir Mark says he came to realise the helicopter was to be used for mercenary activities before the deal was finalised.
Speaking outside court, he said: "There is no price too high for me to pay to be reunited with my family and I am sure all of you who are husbands and fathers would agree with that."
His mother, former prime minister Margaret Thatcher, also expressed her relief at the outcome, adding: "I know that what matters to Mark now is to be reunited with Diane and the children as soon as possible."
Jail term 'reduced'
The BBC's Alastair Leithead said it seemed Sir Mark could now turn "state witness" as part of his co-operation with the South African authorities.
Meanwhile, the Zimbabwean lawyer for a close friend of Sir Mark accused of leading the alleged coup plot, former SAS officer Simon Mann, says that his jail term has been reduced from seven years to four by a court in Harare.
Mann was last year found guilty of illegally buying weapons in Zimbabwe, which were allegedly intended to be used in the Equatorial Guinea coup plot.
A further 14 men were found guilty in Equatorial Guinea of being involved in the alleged plot to overthrow President Nguema, who has ruled Africa's third-largest oil producer for the past 25 years.
Sir Mark, 51, was arrested in August at his home in South Africa and released on bail.
His lawyers have released a statement saying it should be noted he was not charged with any involvement in the alleged coup attempt.