Chairman Rupert Lowe said in a statement on the club's official website: "I regret to inform our supporters that we have today given Wayne Bridge permission to speak to Chelsea Football Club with a view to signing for them.
"Wayne has quickly achieved great footballing success in his time with our club and has served us well.
"He has, however, made it known to both Gordon Strachan and me that he believes a move to Chelsea to be a career progression and an opportunity he cannot turn down.
"He has made it clear that he wants to play Champions' League football, which he believes will give him a better chance of making him first choice for England.
"He will enjoy greater financial rewards at Chelsea and the club is geographically well placed for him to regularly visit his family.
"In the past we have rejected offers for Wayne Bridge from clubs to which he was not attracted.
"He has now handed us a transfer request thereby making it difficult for us to retain him despite the fact that he still has three years remaining on his contract."