Goalkeeper Smith, 18, who joined from Middlesbrough in October, has signed a deal until 2014.
Seventeen-year-old defender Taft, an England Under-19 international, has put pen to paper until 2013.
"This is great news for the club and the players," manager Sven-Goran Eriksson told the club`s official website. "They are very talented young footballers and we have the belief that they will progress, which is why we have given them their first professional contracts.
"It is now time for them to continue to work hard and to fulfil their dreams."
Academy manager John Rudkin added: "Congratulations to them both. I know they will continue to work hard to make the most of the opportunity given to them."
Source: PA
Source: PA