The 24-year-old has four years left on his deal with Leeds, but his contract includes a £20 million relegation release clause which the Blues have now activated.
Chelsea have already agreed personal terms with the midfielder, who is now set to undergo medicals before signing on the dotted line.
Adams only joined Leeds last summer, but his fine performances for the Yorkshire club have not gone unnoticed.
The United States midfielder has been a standout performer for club and country before suffering a hamstring injury in March that ended his campaign prematurely.
He is reportedly nearing a return to training, and the Blues will hope he can pick up where he left off after making a solid impression in 24 appearances for Leeds last term.
Chelsea’s primary defensive midfield target remains Brighton & Hove Albion’s Moises Caicedo, but they are still at odds with the Seagulls over the player’s valuation.
Brighton are standing firm on their £100m asking price, but the Blues are determined to pay a lesser fee for the Ecuadorian midfielder.
Caicedo has already informed Brighton that he wants the move, and Chelsea are preparing a fifth bid for the 21-year-old.
Meanwhile, reports claim the Blues have also lodged a bid for in-demand Southampton star Romeo Lavia.
The Belgian youngster is poised to leave St Mary’s this summer and has been touted for a move to Liverpool, who have already had three bids rejected.
Chelsea are looking to hijack the move and have launched a £48m bid plus add-ons, but Southampton are yet to respond to the offer.
The Blues are determined to sort out their long-term defensive midfield problem this summer.
With Adams now close to signing, it remains to be seen which of their targets will join the United States midfielder at Stamford Bridge.
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