The 19-year-old will miss the opening weeks of the season with a knee injury.
But the Cherries see the England Under-20s midfielder as a long-term investment now they've beaten Wolves to his signature.
Scott played 49 games for Bristol City last season, scoring twice and providing five assists as the side finished 14th in the Championship.
He also won the Under-19 European Championships with his country in 2022.
Scott will become Bournemouth's second most expensive signing in the club's history, surpassing Hamed Traore who joined from Serie A side Sassuolo for £20m after impressive loan spell.
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His fee falls just short of Jefferson Lerma's price in 2018, with him signing for the Cherries for almost £30 million.
According to the Bristol Post, news of Scott undergoing a medical at the Vitality Stadium on Wednesday emerged just before Bristol City knocked Oxford United out of the Carabao Cup with a 5-1 win.
Scott has not played for the Robins so far this season due to a swollen knee, but despite his absence from the 1-1 draw with Preston and the cup win, manager Nigel Pearson has admitted he's 'disappointed' he'd losing his star midfielder.
"I've got nothing to say, really, apart from that the club has given him permission," Pearson said. "Outside of that I've got no comment. I couldn't give you the details… I knew [about the bid] today. And that's it, I'm not saying anymore."
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When pushed on the topic, he added: "I'd been planning to keep him. It's nothing to do with me. It's a club decision.
"I'm disappointed because we've got a better chance of being successful if we keep our best players so that's where I sit on it."
Meanwhile, talkSPORT understands the Cherries are set to hijack Leeds' move for Norwich star Max Aarons.