The Robins had been demanding £25m for the 19-year-old star – who was also attracting interest from Tottenham, West Ham and Wolves.
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But they have now accepted a cut-price of £20m for the young English talent as he prepares to move to the Cherries.
According to Sky Sports, an extra £5m has been tagged on in the form of performance-related add-ons.
He will now “finalise the deal and complete his medical”.
However, he is unlikely to feature for Bournemouth for a number of weeks due to a knee injury.
Scott, who has been dubbed the “Guernsey Grealish”, was crowned the Championship‘s Young Player of the Year in April.
He made 42 league appearances last season, scoring once and assisting five goals for Bristol City.
His impressive form quickly attracted interest from some of England’s top clubs.
European giants Inter Milan were also considering a swoop.
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Earlier this year, Bristol boss Nigel Pearson insisted that Scott will not be allowed to leave the club for cheap.
He told Bristol World: “It’s got to be more than £25million, he shouldn’t go for less than that.
“Since he made his debut for us he’s played 80-odd games, so he’s been a regular.
“People talk about second seasons-itis where players get a drop-off, I don’t think we’ve seen that at all, I think we’ve seen him push on.
“He’s managed to continue his development with a pretty steady upward curve over the two years he’s been here now. That speaks volumes not just about his ability but his temperament too.
“He’ll go on to really big things, I’m sure about that.
“He’ll play at the top, he’ll play for a top side, there’s no doubt in my mind about that, whoever makes a proper bid at some point, it’s going to have to be a really big bid to get him.”
Meanwhile, Tottenham‘s failure to sign target Scott comes just hours after it was confirmed they had agreed a deal to sell Harry Kane to Bayern Munich.
And the inability to beat Bournemouth to a young, promising English midfielder will only anger Spurs fans even further.
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