Mr Shah, who has worked for Fidelity since 1996, will now focus solely on managing the open-ended Fidelity Special Situations fund.
The company hopes Mr Wright's appointment will mean it is able to invest a greater proportion of the portfolio in smaller and mid-cap stocks.
Mr Wright has 10 years experience at Fidelity and has been managing the Fidelity UK Smaller Companies fund since its creation in 2008.
Lynn Ruddick, chairman of Fidelity Special Values plc, said: "The Board is keen to take greater advantage of opportunities for capital growth available from dynamic smaller and mid-cap companies and this is an area where Alex has demonstrated considerable success."

Mr Wright has a contrarian investment style, buying out-of-favour stocks with downside protection and unrecognised growth. This has made him the top performing fund manager in his Investment Management Association UK Smaller Companies peer group.
Ms Ruddick said the investment strategy and company benchmark would remain unchanged.
He said: "We are excited at the opportunity for the Company to broaden its appeal to a wider group of shareholders who are seeking the security of quality large cap stocks as well as the potentially higher growth of carefully-researched companies."
The change will be effective from 1 September.