But the jury at London's Southwark Crown Court failed to reach verdicts on two other charges and were discharged.
Travis, 68, showed no reaction as the verdicts were read out, looking straight ahead.
The jury of eight women and four men had been deliberating for around 20 hours after a trial at 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 February 24 to decide if there should be a retrial of the two outstanding charges.
Travis was allowed to remain seated as the verdicts were passed and listened with the aid of headphones, as he had done during the four weeks of evidence.
His wife Marianne supported him from the public gallery as the verdicts were announced but did not show any emotion.
She sat next to Margaret Merritt, Travis's personal assistant in the 1970s, who gave evidence as a defence witness.
Travis's wife had looked nervous as the jury came back into court.
Judge Anthony Leonard thanked the jury before discharging them and told Travis he would be bailed on the same conditions as before.
"I understand, thank you," Travis replied before leaving the dock.
Asked by reporters if he was delighted by the result as he walked out of court, he said: "No, I'm not delighted at all."
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.
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.
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.
In a statement. Dave Lee Travis said:
"I'm not over the moon about any of this today.
"I don't feel like there is 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, proving the point that not all famous people have got loads in the bank.
"Therefore I had to sell my house in order to do it, but that's OK, I'm not moaning because there are lots of people worse off than me.
"However, I did lose my reputation as well, which I may try and get back later.
"Basically I want to say that I have had two trials. 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 Crown Court.
"All I want to do now is go home and relax with my wife - who has also been suffering through all this with me and been by my side all the time."