The 20-year-old, who was crowned the club's young player of the season, had previously agreed a short-term extension to his contract.
However, it is understood that interest from outside parties has prompted the club to tie the player to a long-term contract.
"I'm delighted to sign a new contract, obviously I had my year extension triggered the other week but I'm delighted to have signed this contract and to be here for at least another two years," he told the club's official website.
"I have been here four years now and I have been enjoying my time here and I am really looking forward to next season. Personally, I have enjoyed my season.
"I have been happy with how I have progressed and developed, I have a lot of developing to do but it's nice to be rewarded for your hard work with a new contract so I am delighted."
Wright has made 40 appearances for the club this season.