The Saddlers are in the process of reshaping their squad following relegation from Division One and recently released nine players.
The pair were two of only a handful of players to be offered new deals, and they have now agreed to the terms put to them by the club's paymasters.
Taylor, 20, claims it was player-manager Paul Merson's declaration that he would give youth a chance next term which prompted him to stay, while Wright, 22, is looking for the chance to help the club bounce back at the first time of asking.
