The BBC radio DJ was arrested in October 2013 over claims he sexually assaulted two teenage boys.
Gambaccini, 69, spent a year on bail before the case against him was dropped in what he labelled a “completely fictitious” affair.
He started legal action against the Crown Prosecution Service last year and has now reached an out-of-court settlement, but confidentiality clauses in the agreement mean the amount paid cannot be disclosed.
Gambaccini was arrested under Operation Yewtree, set up in the wake of the revelations about paedophile Jimmy Savile.
He described the episode as a celebrity “witch hunt”.
In 2015 he said: “The man on the street is known to the people he has met in his life. The celebrity is known to the people he has met in his life, plus millions of others.
“So when you invite the public to accuse a celebrity, you have a pool of people who include not only possibly people who have been abused, but many people to whom a celebrity may have satisfied an emotional need throughout the years even without knowing it. And this is precisely what has happened.”
He said he “wasn’t surprised” to be accused, as he had previously spoken publicly about Savile’s crimes and was once pictured alongside him on a newspaper front page, creating an association in the public’s mind.
Gambaccini had been a fixture on UK radio for decades before the allegations were made.
A CPS spokeswoman said: “We have reached an agreement without admission of liability.”
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