Jurors at London's Southwark Crown Court failed to reach a verdict on two more charges.
Travis had been accused of assaulting young women - at concerts, in radio studios and elsewhere - over a period of three decades.
The 68-year-old had denied 13 counts of indecent assault and one of sexual assault.
Outside court after the verdicts, Travis said he had been through "a year-and-a-half of hell."
"I had two trials," he said. "I 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."
Travis, a longtime radio DJ and host of the TV music show "Top of the Pops," was one of several veteran U.K. show business figures arrested after revelations that the late BBC entertainer Jimmy Savile was a serial sexual predator who abused scores of young people.
Last week the 81-year-old "Coronation Street" star William Roache was acquitted of multiple counts of sexual assault in a separate trial.
Travis - whose real name is David Griffin - told jurors during his trial that he was not a sexual predator, as prosecutors claimed.
"I do not have a predatory nature with women. I have a cuddly nature," he said. "Maybe that's what this is all about, but I am not predatory."
A court hearing will be held Feb. 24 to decide whether Travis will face retrial on the two outstanding charges.
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