Spacey, who was also celebrating his 64th birthday on Wednesday, began to cry and mouthed "thank you" to the nine men and three women jurors, before wiping away tears with a tissue.
The Hollywood star spoke with five of the jurors in the lobby of Southwark Crown Court, before emerging from the building to address a phalanx of journalists and photographers.
"I imagine that many of you can understand that there's a lot for me to process after what has just happened today," he said. "I am humbled by the outcome today."
He also said he was "enormously grateful to the jury for having taken the time to examine all of the evidence and all of the facts carefully before they reached their decision".
Spacey was swarmed by cameras as he then walked to a waiting taxi, as some members of the public clapped and wished him happy birthday and one woman shouted: "We love you, Kevin."
During the four-week trial, prosecutors described the actor as a "sexual bully" who had aggressively groped three of the men and performed oral sex on the fourth while he had passed out in Spacey's London apartment.
Spacey, tried under his full name Kevin Spacey Fowler, said in evidence that the case against him was weak, and that the incidents, if they had occurred at all, were consensual. He said he was promiscuous, a "big flirt" who had "casual, indiscriminate sexual encounters".
One of complainants alleged Spacey painfully grabbed his crotch like "a cobra" in the mid-2000s, an allegation Spacey described as "absolute bollocks", using a British slang term for testicles and for something which is nonsense.
While he said he might have made a clumsy pass at one of the men, he said he had never assaulted anyone and suggested that the accusers had come forward to make money.