The Leeds United midfielder is expected in London on Thursday to undergo a medical, and Chelsea are hopeful he can be registered in time to be available for Sunday's Premier League opener against Liverpool.
Leeds did not want to lose Adams, but the clause in his contract became active when the Yorkshire club were relegated from the Premier League last season.
Adams, 24, only signed from RB Leipzig in July 2022 and made 26 appearances in all competitions, partly due to his season ending prematurely in March because of a hamstring injury that required surgery.
Adams will strengthen an area of the pitch where new head coach Mauricio Pochettino has been desperate for reinforcements, having allowed N'Golo Kante, Mateo Kovacic, Ruben Loftus-Cheek and Mason Mount all to depart in addition to Denis Zakaria returning to Juventus following a loan spell.
Meanwhile, Chelsea continue to pursue a deal for Brighton's Moises Caicedo after seeing their first two offers rejected, the latest of totalling £80m. Brighton are continuing to demand in excess of £100m.
Liverpool are also interested in Caicedo and in addition, the two clubs are battling each other for Southampton's Romeo Lavia.
Liverpool had a £45m bid dismissed by Southampton for Lavia, with his asking price set at around £50m while Chelsea closely monitor the situation.