Thatcher, the son of former British Prime Minister Margaret Thatcher, avoided a prison sentence by entering a plea bargain with South African authorities, the BBC reported. He was fined $474,000 and given a four-year suspended sentence.
He will now be able to leave South Africa for the first time in five months.
Speaking outside the court in Johannesberg, Thatcher said: "There is no price too high for me to pay to be reunited with my family and I'm sure all of you who are husbands and fathers would agree with that."
Thatcher continues to deny any knowledge of the plot though he admitted breaking South Africa's anti-mercenary laws by agreeing to charter a helicopter. The businessman has reportedly said he believed the helicopter was to be used as an air ambulance.
Equatorial Guinean authorities are likely to continue pressing for the chance to question Thatcher. Fifteen men have already been found guilty of involvement of the alleged plot to overthrow President Teodoro Obiang Nguema Mbasogo last March, including former SAS officer Simon Mann, a close friend of Thatcher's believed to have led the group.