The 84-year-old, giving evidence for the first time, also sang some of his trademark song Jake the Peg to the courtroom.
Harris told jurors at Southwark Crown Court that he was left feeling “sickened” by his behaviour, blaming himself for the alcohol problem the woman developed.
But he insisted their affair was “consensual” and she was a “willing participant” in the string of sexual encounters they had.
Harris faces 12 counts of indecent assault on four alleged victims between 1968 and 1986, all of which he denies.
The artist rebuffed all the allegations, including claims from his daughter’s friend which relate to seven counts. But he admitted they had had several intimate encounters beginning when she was around 18.
He also revealed that he had a second affair, this time with a woman that he and wife Alwen had allowed to live rent-free in an annexe at their home. His wife listened from the public gallery alongside other family members as Harris told how she was “devastated” when she found out.
When questioned about the allegations relating to his daughter Bindi’s friend – which the alleged victim claims date back to a holiday in Hawaii when she was 13 – the TV personality said their relationship only began when she was an adult.
The entertainer told the court: “It was all consensual and everything that had happened, she had been a willing participant.”
But the 84-year-old, who started giving evidence standing, but later sat in the witness box, told the packed courtroom: “I felt that I had betrayed everybody. Betrayed their trust.”
Pressed by his defence barrister Sonia Woodley QC on why he felt such remorse, Harris’s voice broke as he told jurors: “Because I’d had an affair with their daughter, who was much younger than me. An extra- marital affair.”
Harris said he felt “sickened by myself for being a part of it at all”, adding: “I knew it was wrong. Here I was, much older than her. A very young lady who was many years my junior.”
Harris said he originally told police there had only been two sexual encounters between him and the girl because he felt “huge embarrassment” about it.
The star told the court that the pair’s first intimate encounter happened when she was 18 as he took her a cup of tea in bed when she stayed at his home in Bray, Berkshire.
He described how she appeared to “invite” him to touch her, behaving in a “flirtatious” and “coquettish” way.
Harris, who earlier admitted he was “touchy-feely”, described how his “heart was thumping” as he touched the girl’s leg, before leaving the room.
“I find it very hard to discuss this. It’s embarrassing. A married man, a much younger girl, I shouldn’t have been doing it.” He added: “It seemed to be an invitation, shaking off the duvet.”
The encounter marked the start of a series of sexual trysts between the pair, Harris said, in which he claimed she was always a willing participant, even instigating some of the encounters. Later, after receiving several “unintelligible phone messages” from the woman, Harris visited her at her parents’ house in Norfolk. He said: “She was blaming me for the state she was in, destroying her life, she said.
“I felt I had let everybody down, I felt I had let Alwen down, and Bindi down and [the alleged victim’s] parents down, so I said ‘Please forgive me’, and she said, ‘I forgive you’.”
The woman asked for £25,000 so she and her boyfriend could open an animal sanctuary, he said. When he refused, she became “irate”, beating him with clenched fists, and told him: “You’d better keep your eye on the weekend papers”.
The court also heard that Harris embarked on a second affair with a woman he and his wife allowed to stay in an annexe they built for their daughter in around 1995-96. He said they allowed the woman, who was “down on her luck”, to stay rent-free, but a relationship developed between him and her.
During his first day in the witness box, Harris also outlined his rise to stardom, describing how he had created his famous “wobbleboard”, and even singing a segment of his hit song Jake the Peg. Harris had to be interrupted several times by Ms Woodley as he appeared to get carried away with his reflections.
The trial continues.