Watford Chairman Graham Simpson said in a statement: "It is with great regret that the board have accepted West Brom's offer for Paul.
"No decision like this is taken lightly, but given our current position a six-figure sum represents significant income.
"This offer was totally unsolicited, Paul wasn't looking for a move and we weren't looking to move him on.
"Obviously this is not something Ray Lewington would want to do in an ideal world, but he understands the reason behind the decision, which was made by myself and the board."