"I'm having the time of my life," he said, having raced around the track himself.
"I'm a little giddy right now. It's great to be here. We're having such a laugh. It's the time of my life.
"To be a part of it in this way? To tell our story? Everyone has been cool with us, the teams have opened their doors to us, the FIA have been really helpful, F1 and Stefano Domenicali. Everyone has been amazing."
And he received a warm reception from the drivers when he and director Joseph Kosinski joined the drivers' briefing ahead of the race.
Seven-time champion Lewis Hamilton of Mercedes, who is an executive producer for the film, said it was "probably the best drivers' briefing we've ever had."
In the film, Pitt plays a veteran driver who joins an F1 team represented at Silverstone by a fictional 11th team on the grid, complete with a garage and pit-bay alongside Ferrari.
Using Formula Two cars converted by Mercedes, the film cars took places on the grid for the race and ran in part of the formation lap before the start of the Grand Prix.
They were driven by former drivers Craig Dolby and Luciano Bacheta.
Mercedes' George Russell said it had been a surreal experience to share space with Pitt.
"It's one of those you see a worldwide superstar for the first time – it's quite surreal. It's only when you get to be with those individuals whether it's Tom Cruise, Brad Pitt or Roger Federer that you recognise they're just normal human beings.
"He was joking around and having a good time and just kind of one of the boys really. I'm so excited to see what the movie does."
Ferrari's Charles Leclerc and Alpine's Pierre Gasly were among the drivers thrilled by their chance to spend time with Pitt, but defending world champion Max Verstappen said he was less than impressed.
"I think they're going to use some shots of everybody, in terms of on-board cameras and stuff," he said. "I completely can't be bothered with this.
"In the end, a film is always made to create a little bit of a show because, of course, it won't all be real, but I think it's all fine. I'm actually not that much into it."