Johnny Depp was always considered an oddball by Hollywood studios. The dark and edgy art-house films that Depp preferred were regarded as “box-office poison”. Even when he had his big-money break, in Pirates of the Caribbean, he was almost sacked after two weeks for playing his role as Captain Jack Sparrow like Keith Richards of the Rolling Stones.

But what a turnaround. Depp, 44, one of the coolest men in Hollywood, has been voted the top moneymaking star by American cinema owners. The success of the three Pirates films, which runs to several billion dollars, makes him the hottest act in town. He’s also among the favourites to pick up the best actor award at this year’s Oscars for his starring role in the horror musical Sweeney Todd: The Demon Barber of Fleet Street, for which he bagged a Golden Globe.

Suddenly it seems he can do no wrong. Even Tim Burton, who directed Depp in Sweeney Todd, their sixth movie together, is mystified. “I never thought I would see the day when a major film studio allowed me to make an 18-rated musical with a lead actor who has never sung in his life.”

But Depp, despite admitting some trepidation about the singing – “I had never even sung in the shower. I would be too mortified” – seems to take it, along with everything else, in his stride. As he sits in a London hotel suite, his slight frame, chiselled features, dark hair and moustache give him the air of someone a decade younger.

Living at full throttle hasn’t given him so much as a grey hair. Life in the fast lane on the road includes ownership of Harley-Davidsons, a customised 1960s 650cc Triumph Bonneville motorcycle and a Norton Commando. Outside his Hollywood home is a sporty Porsche 911 Carrera, but he admits his priorities are changing. “I’ve always liked speed, but now I like comfort,” he says. “We all go through the stage of wanting the fast cars and bikes. I was no different. Who wouldn’t admire a Maserati? But I also wanted to ride in style, or with a bit of history. To get there – and enjoy the journey.”

He finds the comfort zone in his modest Mercedes-Benz A-class, the same model he reversed into the gates of his French country home on the Côte d’Azur a couple of years ago. He shares car and home with his girlfriend, Vanessa Paradis, and their children, Lily-Rose, 8, and Jack, 5. His family has changed his life. He became mainstream on screen and in his private life at about the same time. “I have learnt to grow up and still enjoy myself,” he says. “I spent a lot of years living on the edge – everyone knows that. So it’s good that I live calmly and happily.”

In March last year that new-found happiness almost deserted him when Lily-Rose was admitted to Great Ormond Street hospital in London while he was filming Sweeney Todd. She had contracted an E. coli bacterial infection, her kidneys were beginning to shut down and Depp thought they might lose her. Last week he donated £1m to the hospital as a thank you for saving her life and in November he spent four hours at the hospital, dressed as Captain Jack Sparrow, telling bedtime stories to patients.

He is clear about what his family life in France has given him, after a childhood spent moving around with his mother, Betty, a waitress, his father, John, an engineer, and his three siblings. “I have never felt more rooted anywhere,” he says. “I have never been in one place, like this, where I felt completely at home. Los Angeles was my home from the early 1980s to the late 1990s but it still felt transient compared to this.”

He certainly lived the life in Hollywood. He owned the infamous Viper Room nightclub when River Phoenix died outside it from a drugs overdose. While still trying to make it in his first career as a wannabe rock star, he was married, at 20, to Lori Anne Allison, a make-up artist, whom he divorced in 1985. He has been engaged to more famous women than possibly any other actor, including Winona Ryder and Kate Moss. He trashed his room at the expensive Mark hotel, New York, after an argument with Moss, and ended up in jail.

He made news for all the wrong reasons, while delivering films such as Edward Scissorhands, What’s Eating Gilbert Grape?, Ed Wood and Don Juan DeMarco. They established his acting credentials but failed truly to light up the box office. It did not seem to bother him. “One consistent theme in all the characters I play is that they are considered freaks, but to me they are real people,” he says. “They feel love, anger and loneliness. Why am I attracted to those parts? I identify with them. I am attracted to emotions. I then watch the film once or twice and let it go. After my job is done, it is almost none of my business. The director decides what is used and how.”

His title role in Sweeney Todd, which opens in UK cinemas on Friday, is garnering him some of the best reviews of his career. It is based on the award-winning musical composed by Stephen Sondheim. Depp plays Benjamin Barker, a high-class barber, who returns to London swearing revenge after being imprisoned for 15 years on trumped-up charges because a judge, played by Alan Rickman, wanted him out of the way so he could steal his wife. He opens a barber’s shop and sets about cutting the throats of his enemies, aided and abetted by Mrs Lovett, played by Helena Bonham Carter, Burton’s girlfriend, who uses the human flesh as filling for her famous pies. It seems right up Depp’s street, with its heavy gothic overtones, much flashing of open razors and blood by the bucketload.

Now Depp is no longer struggling with the teenage demons that left him with several self-inflicted scars. “I felt weird at five,” he says. “Yes, it’s true. At the age of 12, I felt it was me against the world. I remember locking myself in my bedroom and playing my guitar. It seemed as if I was in there for about two or three years. The most important thing is that now, at least, I feel comfortable with myself. I do not have to pretend any more about who I am. I do not want to portray any image that is not myself.”

My stuff...

On my CD player Everything from the early Rolling Stones, Iggy Pop and Billy Idol to reggae and African music

On my DVD player Films featuring Marlon Brando, who had the right perspective on the Hollywood industry from day one

In my parking space A Mercedes A-class

I would never throw away Photographs of my children