The Man Utd manager learned on Sunday he would not face any action after 21-year-old student Nadia Abrahams claimed he had repeatedly touched her leg.
In a statement, Ferguson said: "I welcome the decision of the director of public prosecution, advocate S W Kahn (senior counsel), not to institute a prosecution against me.
"I am extremely appreciative of this swift but no doubt thorough and decisive way in which the South African police services and advocate Kahn dealt with the matter.
"I thank all those who believed in my innocence and have supported me during this time.
"I want to make it clear that this matter will not deter Manchester United or myself from concluding the business for which we came to South Africa, namely to build bridges between South African football academies and Manchester United."
South African police described claims that Ferguson repeatedly touched Abrahams' leg in Cape Town on Friday as "ridiculous".
"We feel our time and everybody else's has been wasted," said Sipho Ngwema, a spokesman for the national director of public prosecutions.
"There are no grounds for prosecution."
Ngwema added that the authorities would consider taking action against Abrahams.
"We will look at it in due course," he said.
In an interview with the Mail on Sunday newspaper Abrahams accused Ferguson of "repeatedly squeezing her thigh" as she drove him back from the jazz club.
She said this caused her to swerve off the road and puncture a tyre on the kerb.