The United States international has been keen to remain in the Premier League after Leeds were relegated to the Championship last season.
And a host of clubs had been interested including Chelsea and Liverpool but Bournemouth appear to have won the race.
talkSPORT understands that Adams is undergoing a medical at the Vitality Stadium ahead of a move to the south coast.
The midfielder has a £20million release clause that became active after Leeds were relegated.
Adams made 26 appearances across all competitions for the Whites in an injury-ravaged campaign in the Premier League.
READ MORE ON TRANSFERS
Chelsea spending under Boehly moves closer to £1bn with Lavia transfer the latest deal
Mikel Arteta hints at further Arsenal transfers to cover for injured Jurrien Timber
But the former RB Leipzig star was one of the better performers in a horror season for Leeds, who sacked two managers in the process in Jesse Marsch and Javi Gracia.
The deal has not been without its problems, though, after Leeds insisted that Adams' release clause had expired.
However, that appears not to be the case as Bournemouth push forward with a medical.
And the player himself must be feeling dizzy after having a transfer to Chelsea fall through earlier this month.
Most read in Football
Chelsea confirm Lavia, Liverpool prepare Gravenberch bid, Paqueta to Man City off
Reason why Nottingham Forest vs Sheffield United is not on TV this Friday night
Chelsea announce Lavia move to complete Liverpool hijack and take spending close to £1bn
Former Arsenal star Walcott announces retirement and thanks two managers in farewell video
The Blues were keen on snapping up the American to add depth to their midfield.
But after finding that he is currently sidelined for several months, Chelsea pulled the plug on a deal.
Liverpool were also interested after missing out on Moises Caicedo, who did end up at Stamford Bridge.
Adams has already missed a sizeable chunk of the year after undergoing surgery in March.
Bournemouth have themselves splashed the cash in a bid to underline their Premier League position, which also included the dismissal of Gary O'Neill.
Ambitious owner Bill Foley has already signed seven players in Alex Scott, Max Aarons, Romain Faivre, Justin Kluivert, Hamed Traore, Milos Kerkez and Ionut Radu.
And Andoni Iraola has been hired to bring an expansive and attractive brand of football to the Vitality Stadium.