Daniel Okev, a 45-year-old retired major, shot Mr Hunter, 22, and wounded Charlotte Gibb, 20, after giving them a lift from the Red Sea resort of Eilat 10 nights ago. He was arrested at his home near Tel Aviv early yesterday after an intensive manhunt by a team of about 100 detectives, undercover officers and forensic scientists.
Mr Okev, who is married with two children, was remanded in custody for 15 days by a Beersheba magistrate. When the police picked him up, he said: "I was expecting you."
A police spokesman said Mr Okev, who works for a private transport company, could not explain why he had shot Mr Hunter. Police praised Miss Gibb for her courage, after she was hypnotised to provide details of the murderer.
News of his arrest came as she prepared for a visit from Mr Hunter's parents - their first meeting since the attack - at Addenbrooke's Hospital, Cambridge, where she is recovering.
"She is quite prepared for the meeting," said David Adlam, an oral and maxillofacial consultant. "I think if anything she is more concerned for them than she is for herself."
Mr Adlam talked in detail yesterday for the first time about Miss Gibb's injuries and her "million-to-one" escape. He said the bullet which went through her face had amazingly done very little damage.
"I think it's fair to say it's a miracle really. The bullet managed to miss every vital nerve in her face," he said. "Had the trajectory been altered by millimetres it would have gone straight into her brain and killed her. I think it must be a million-to-one chance."
Her parents had been with her constantly in shifts, Mr Adlam said.
"Psychologically she is just starting to come to terms with it ... she is in excellent spirits, but it is only a week or so after the event and she is only really starting to come to terms with the whole thing," he said.
Before returning to England, Miss Gibb was interviewed under hypnosis, and gave the investigators information about a grey-haired man in his forties, which helped the police to build up a profile of the killer.
The police chief for southern Israel, Commander Danny Brinker, commended Miss Gibb for her courage.
The breakthrough came when a policeman at a checkpoint, set up after the murder was discovered, remembered a red Peugeot 309 crossing the border back from Eilat to the twin Egyptian resort of Taba. The driver had slipped through while the policeman was questioning another motorist.
Police believe that Mr Okev had been to the casino at the Taba Hilton and was returning to his home, 300 miles north of Eilat, when he picked up the British couple at a petrol station around midnight on 13 August. He suddenly shot them after stopping for a cigarette on the Negev desert road. According to the police, he drove back to Taba and slept the night in the hotel.
Detectives traced the car to Mr Okev's home in the commuter village of Even Yehuda, north-east of Tel Aviv. The car and its owner were kept under surveillance. Police secretly searched the car and found Mr Hunter's fingerprints inside. Ballistics experts identified a licensed gun owned by Mr Okev as the murder weapon.