The Blues have been in advanced talks with the versatile defender, who will become a free agent tomorrow.
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The 24-year-old, who is primarily a right back, has played 69 Premier League games for the Hammers and also featured in the Europa League and Conference League.
He can also operate at left-back and in more advanced wide positions too, with Blues boss Kieran McKenna known to be be keen on his players having versatility.
Johnson rejected a new five-year contract from the Hammers earlier this month, and has also been linked with Crystal Palace, Everton, Wolves, Southampton, Rangers and Leeds.
West Ham posted on X this morning to say: “West Ham United can confirm that Ben Johnson & Divin Mubama
“We would like to thank both players for their hard work and commitment during their careers in Claret and Blue and wish them the very best in the future.”
The Blues agreed a club record deal to sign dynamic young attacker Omari Hutchinson from Chelsea on Friday, subject to his medical.
Town return to start pre-season training ahead of their Premier League campaign tomorrow.