If your dad is a Hollywood director, your mother a screenwriter and your big sister a star married to another star, it might seem natural that you'd grow up wanting to be in films.

"Not so," says Jake Gyllenhaal, giving me that blue-eyed mock-surprised smile that seems to win over audiences so effortlessly. "There's a very early entry in my diary from when I was six years old that said, 'Soccer is my life.' It was my obsession at school. I couldn't wait for class to be over. I played in all positions because at that age there isn't really a position, you just run after the ball."

So when did he decide he mightn't have what it takes to go all the way as a footballer, opting instead for acting? "I didn't. I still dream of making the American World Cup team. I'm hoping to watch them play in South Africa. People used roll their eyes in a condescending way when I talked up their chances but this time they really are contenders. I'm proud to say I support them."

If his soccer dream didn't come true, another dream has. He's set to emulate Johnny Depp's success in The Pirates of the Caribbean franchise as the latest Jerry Bruckheimer swashbuckling action hero in Prince of Persia, which opens worldwide this week. "It's like fulfilling a fantasy I had when I was eight. What young boy doesn't think, while playing with an action figure, that maybe one day...?

"If you were to go back to the me that was then and say, 'You're going to be in a movie that looks a little like Indiana Jones and it's from a side-scrolling action game called Prince of Persia you're actually playing on that weird thing called a computer', I think my head would have exploded."

Not that Gyllenhaal got ahead of himself as a child. To remind him of his privileged upbringing – he was taught to drive by family friend Paul Newman – his liberal parents made him celebrate his bar mitzvah at a homeless shelter in Los Angeles. He had fun playing bit parts in some of his father Stephen Gyllenhaal's films, most notably along with his sister Maggie in A Dangerous Woman (which was written by his mother Naomi Foner, best known for Running on Empty). But apart from playing Billy Crystal's son in City Slickers when he was 11 he wasn't allowed to take up offers from other film-makers: instead he followed Maggie to Columbia University, where he studied Eastern religions and philosophy.

His first lead role was in October Sky in 1999 as a southern boy with a talent for rocket science who tries to win a college scholarship to avoid working in the West Virginia coal mines like everyone else in his family. He caught critical attention in the Richard Kelly cult hit Donnie Darko as a troubled teenager who imagines a six-foot rabbit called Frank has told him the world is about to end. Maggie played his sister: their good-natured sibling rivalry had become a spur to him making it as an actor. "That's what brothers and sisters are like; there's always going to be some competition and rivalry."

Just as Maggie (who is married to Peter Sarsgaard) quietly established herself in indie hits like Secretary before stepping into higher-profile Hollywood roles like Mona Lisa Smile, Jake worked his way up with serious dramas like The Good Girl and Jarhead – and won the Evening Standard's Outstanding Newcomer Award with his 2002 stage debut in Kenneth Lonergan's This Is Our Youth – before picking up an Oscar nomination in Ang Lee's groundbreaking Brokeback Mountain, starring with Heath Ledger as a couple of cowhands who become involved in a secret sexual relationship. Gyllenhaal, who is godfather to Ledger's daughter by Michelle Williams, famously described their male screen intimacy as "doing a sex scene with a woman I'm not particularly attracted to".

But the little boy daydreaming of action heroes never went away. He toyed with an offer to take over from his friend Tobey Maguire in Spider-Man 2 before playing Dennis Quaid's marooned son in Roland Emmerich's apocalyptic doomsday blockbuster The Day After Tomorrow, which grossed nearly $550m worldwide. When Jerry Bruckheimer wooed him with Prince of Persia, there was never any chance of him not saying yes.

"People tend to associate starring in films like Prince of Persia only with commerce," he says. "For me it was always a sense that it just was so fun to be in a fantasy adventure as a street kid who is adopted by a Persian king as his heir to prevent his sons fighting over the throne – and to then team up with a feisty princess against dark forces to safeguard an ancient dagger capable of releasing the Sands of Time. I looked at it as if I were reading a children's book to a child. 'And then the robbers came in... And the bad guys turned up.' It was that kind of acting. And there was the whole thing every day where I would drive to work and it was like going to a sporting event where you're captain of the team arriving at these huge sets over 100 feet high, all built with perfect detail, something you don't see anymore when you go on a set because most of the stuff is green-screened and then put together later. I felt like a kid every day."

Gyllenhaal argues that roles like Prince of Persia – it seems destined to become a franchise: he's signed up for sequels – don't come out of the blue. "I believe you earn your stripes," he says. Sam Mendes cast him as the aggressive US marine in Jarhead after seeing him on stage in This Is Our Youth. "I don't think I'd realised until then how tall and masculine he is," marvelled Mendes. "He's a big guy and he has a combination of soulfulness and man of action." Jerry Bruckheimer said, "He's an actor I've been watching and wanted to work with for a very long time." Director Mike Newell was also a fan. "He'd worked with my sister Maggie and had seen and respected my work," says Gyllenhaal. "It wasn't just by chance. I worked to earn their confidence in me. That's how it should be, rather than suddenly saying this person is the thing, NOW!"

Gyllenhaal entered into the spirit of the film, putting on muscle, fight-training, sword-fighting, learning parkour (running up walls) and horseriding. He's since lost the pin-up biceps. "I like to cycle and run long distances, but being in shape is different things. Lance Armstrong doesn't look fit in the way other people are but he has the strength to win the Tour de France. For me being in shape is feeling great."

So how did he prepare for playing the wayward alcoholic jailbird brother of war hero Tobey Maguire in Jim Sheridan's Brothers? "Well, I think you've just answered that in the way you phrased the question," he laughs. It seems what helped him most was Sheridan's gruff advice: "Jake, I just want you to know, you're playing my little brother so I'm going to have to hate you most of the time."

"I go after these things and I want to do things that I'm into and I'm inspired by," says Gyllenhaal. "I play a Viagra salesman in a movie I've just finished called Love & Other Things. The research for that was" – he pauses teasingly – "interesting."

Not that filming is all fun. During the Bush years he campaigned for civil liberties and starred in Rendition with Reese Witherspoon (with whom he had a two-year relationship). Films were filling the gap left by the failure of the media to question what was happening, prompting his remark that "it's a sad time when actors are politicians and politicians are actors". Has the election of Obama changed this? "We now have a smart, clear-thinking adult leading us who makes me feel that all actors can be actors again."

Gyllenhaal will be 30 on 19 December. "Up until now I haven't really been so clear about all the things I wanted to be or who I was. I think now I feel much more comfortable with it. I enjoy laughing and I want to make movies that are like that. The thing is, I've always wanted to be older."

'Prince of Persia' opens on Friday