The 68-year-old broadcaster was acquitted of 12 abuse charges at Southwark Crown Court. But the jury failed to come to a decision on the two remaining assault cases – including one involving a journalist in 2008.
The broadcaster said he had been forced to sell his house to pay for his legal costs.
A further hearing will be required to determine whether he will be retried on the remaining counts.
Speaking to the media from the steps of the court he said: “Basically, first of all, I'm not over the moon about any of this today.
"I don't feel like all there's a victory in any way, shape or form. On the contrary, I think you already know that I have been through a year and a half of hell on this which included costing me so much money to pay out for my part of this trial."
He added that he felt he had been through two trials.
He said: "I have had one trial by media and one trial by Crown Court.
"And I have to say, in all honesty, that I prefer trial by the by Crown Court.
"All I want to do now is go home and relax with my wife who's also been suffering through all this with me and been by my side all the time."
Travis showed no reaction as the verdicts were read out, looking straight ahead and listening with the aid of headphones, as he had done during the four weeks of evidence.
The jury of eight women and four men deliberated for around 20 hours after a trial in which the former Top Of The Pops presenter was accused of indecently assaulting 10 women and sexually assaulting another in alleged incidents dating back to 1976 when he was at the height of his fame.
There will be a further hearing at the same court on 24 February to decide if there should be a retrial of the two outstanding charges.
Today's verdicts come a week after Coronation Street star William Roache was cleared of a string of sex offences, prompting claims that he had been the victim of a "celebrity witchhunt" in the wake of the Jimmy Savile scandal.
Prosecutors alleged that Travis was an "opportunist" who assaulted "vulnerable" young women while working at the BBC and commercial radio.
Travis was found not guilty of indecently assaulting nine women, but jurors failed to reach verdicts on the alleged indecent assault of a woman working on a pantomime in the early 1990s along with an alleged sexual assault on a journalist who interviewed him at his home in 2008.
Jurors cleared him of groping a teenager in his Radio 1 studio in the 1970s, a 15-year-old girl at a Showaddywaddy concert in 1978, and a teenage music fan during an episode of Top Of The Pops in 1978.
He was also found not guilty of grabbing the breasts of a Radio 4 announcer in the early 1980s, a teenager in his motorhome at a gig in 1983, and a young hotel worker in Bude, Cornwall, in 1984.
The other charges he was cleared of were two counts of assaulting a British Airways worker in the 1990s and four that related to two women he worked with when he had a slot on Classic Gold radio in the early 2000s.
Giving his own evidence, Travis – on trial under his birth name David Griffin – told jurors that he was not a "sexual predator" and the claims against him were "nonsensical".
"I do not have a predatory nature with women, I have a cuddly nature. Maybe that's what this is all about, but I am not predatory," he said.
Travis also said he would have reported Savile to police if he had known the television star was a paedophile, but denied the two had ever been close.
The defendant was supported by a host of defence witnesses during the case, including Chuckle Brothers Barry and Paul Elliott, Patricia "Dee Dee" Wilde of Top Of The Pops dance troupe Pan's People, and former colleagues at the BBC and elsewhere.
His wife has been in court to support him since the jury retired to consider its verdicts on Monday.
She did not attend the rest of the trial, with Travis telling jurors he did not want her to give evidence as she has "suffered enough nonsense".