Reports this week emerged claiming that the League One outfit had accepted a £1m bid from Middlesbrough for the 25-year-old.
Head coach Sean O'Driscoll said: "We are sorry to see Albert go, but his departure is not a surprise and we have been planning for it all summer.
"If he had stayed it would have been fantastic but we totally understood his situation and had to act in the best interests of the club.
"I cannot fault Albert's attitude over the past couple of weeks. It would have been easy for him to be distracted by the uncertainty of his own future but he never let that affect him in training or the two friendly games he played. We wish him all the best."
Adomah has signed a three-year contract with Middlesbrough.