And it's not the only pop song to have been adopted by England fans.
"I've never seen anything like it!" cried former England footballer Micah Richards on BBC Radio 5 Live on Wednesday.
Over on ITV, another former England player-turned-pundit, Gary Neville, soaked up the joyful atmosphere in Wembley Stadium and declared: "This is one of the best experiences I think I've had in football."
They weren't speaking after England's men qualified for their first major final since 1966.
They were talking before the semi-final, when 60,000 people were belting out Sweet Caroline as the teams prepared to take to the pitch.
A couple of hours later, the song blasted out of the speakers again, and this time the whole squad linked arms and jumped up and down as they joined in the euphoric chorus.
Somehow, a song first released by an American soft rock star in 1969 has suddenly been adopted as England's new sporting anthem.
"There are certain songs that you go, 'I completely get why this is being sung en masse,'" says actor Steve Furst, who performs a Neil Diamond tribute act.
"And a song like Sweet Caroline is in no way a surprise because the Diamond appeal is that he doesn't overcomplicate anything. That very simple sing-along chorus just makes it perfect, and everyone knows it."
Paul Carr, professor in popular music analysis at the University of South Wales, who wrote a recent article about what makes a great tournament anthem, adds: "It's a song that's got a lot of nostalgic resonance for many of the people who sing it.
"The big thing is simplicity of the melody, and there's something in the lyrics."