He vanished without explanation before a mixed doubles match on Monday and his family called police and hospitals when he failed to return to their rented house. Wimbledon fined him pounds 630 for the default.
His mother Patricia, who is staying with Murphy's brother Luke at the house near the All England Club, said: "He is safe and well. He telephoned his sister (Rachel) in Atlanta to say he is in London. He didn't make his match yesterday and he was defaulted and he decided to go off. We are not concerned about his safety any more, but we want to know exactly what happened."
She declined to reveal her son's exact whereabouts in London. "We are just very pleased. With all the foolish rumours circulating it wasn't a restful night. At least we know he is safe and well."
Later, the family issued a statement saying: "We simply want everyone to know that Murphy has taken a few days by himself in the country to relax." The statement said the family would make no further comment during the tournament.
Luke Jensen said his brother slept through a match during a recent tournament in Nottingham but he said he didn't have the "faintest" idea why his brother would skip out of Wimbledon.
"I know him as good as anybody," he said. "I travel with him every day, practice with him every day. He just kind of vanished. That's the big question mark he has to answer.
"It's so out of character. He is spontaneous, very creative. But he's very responsible. He usually calls and lets us know."
Luke Jensen dismissed reports that his brother had considered suicide. He also played down speculation that Murphy wanted to avoid drug-testing.Reuse content