The 68-year-old - whose numerous Hollywood roles include appearances in the Bourne and X-Men franchises - admitted he is very much in favour of Scotland becoming an independent country, but said of Britain, "We're part of the same... we're brothers."
Cox - who starred as William Wallace's uncle in Mel Gibson's Braveheart - said of the referendum: "It means a lot. It's something that I've come to very late in life.
"It's based on my own history and having lived in 'North Britain' as a wee boy, and having seen Scotland become more and more its own country. I never ever thought I'd feel this way, but I'm for it."
He went on: "But that being said, it doesn't mean that we're separate. We're part of the same... we're cousins, we're brothers, we still are.
"It's not an anti-English thing, none of that. It's about separate autonomy which is different. And that's what gets confused in people, they think it's something about, 'We don't want England.' It's not about that.
"What we want is democracy, what we want is egalitarianism and what we want is certain things that have been missing down here for quite a while, particularly in the regions of England.
"And I come to Scottish independence from very much the position of being an Anglophile. Actually it's as much about England as it is about Scotland."
Cox stars as former Manchester United manager Sir Matt Busby in new film Believe. Busby, who died in 1994 aged 84, famously cheated death in 1958 when he and his team were involved in a plane crash in Munich.
Set in the early 1980s, the fictional film sees Sir Matt come out of retirement to coach a team of young working class boys for an upcoming local league cup.
Cox said of the role: "When you play somebody who's famous you want to get your own view of them and get in their skin and get in their essence.
"And it was just an honour to play somebody like Matt because of his history and what he did, and then this extraordinary tragedy that happened to him
"So from an actor's point of view it was tremendous fuel. I loved the whole notion of Matt and I remember my own feelings about him, because he was quite a hero figure for me as a child in Scotland. So it was a joy."