Jurors at his trial failed to reach verdicts on two other charges and were discharged.
The jury of eight women and four men had deliberated for more than 20 hours at Southwark Crown Court, London, on the charges, which dated back to 1976 when Mr Travis, now 68, was at the height of his fame.
He 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.
Mr Travis was released on bail until a further hearing, to be held on February 24, while the Crown Prosecution Service decides if there should be a retrial on the two outstanding charges.
The counts the jury could not decide on were an alleged indecent assault on a woman working on a pantomime in the early 1990s and an alleged sexual assault on a journalist who interviewed Mr Travis at his home in 2008.
But Mr Travis, who admitted to cheating on his wife Marianne of 40 years, said he did not regard the verdicts as a "victory".
Speaking outside the court, he said the case had cost him his reputation, along with so much money that he has had to sell his house.
Flanked by Marianne, Travis, real name David Patrick Griffin, said: "Basically, first of all, I'm not over the moon about any of this today.
"I don't feel like 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 he felt he had been through two trials.
"I have had one trial by media and one trial by Crown Court," he said. "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."
He declined to answer questions about whether he felt he had been the victim of a "witchhunt" against famous people accused of sexual crimes. The verdicts came a week after Coronation Street star William Roache was cleared of a string of sex offences.
Mr Travis, from Buckinghamshire, was arrested under Scotland Yard's Operation Yewtree, which was prompted by abuse allegations involving the late Jimmy Savile, who presented Top Of The Pops and Jim'll Fix It.
Prosecutors alleged Mr Travis was an "opportunist" who assaulted "vulnerable" young women while working at the BBC and commercial radio.
Jurors found him not guilty 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 cleared 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 Cornwall, in 1984.
The other charges he was found not guilty 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 last decade.
Detective Chief Superintendent Keith Niven, who is leading Operation Yewtree, said "We fully investigate every case and once sufficient evidence is obtained investigators work with CPS lawyers and a decision whether to charge is made.
"In the case of Mr Griffin, the prosecution was brought, he was tried and the jury reached their decision.
"We encourage victims to come forward and pledge our commitment to support anyone who has been subjected to sexual abuse.
"We continue to work closely with our partners and dedicate resources to investigate crimes of this nature.
"We will ensure all victims have a choice."
A CPS spokesman said it was considering whether a retrial would take place, adding it would be inappropriate to comment further while proceedings were still active.