Mr Bolton has been managing China Special Situations fund since April 2010 and prior to that he managed the Fidelity Special Situations fund from 1979-2007.
Mr Bolton will remain as an adviser to Fidelity and a trustee of its charitable foundations.
He will replaced as manager by Dale Nicholls from April 2014 and the pair will work closely together to ensure a smooth handover.
Mr Nicholls has been running the Fidelity Funds Pacific Fund since September 2003 and has 17 years investment experience.
Fidelity said that Mr Nicholls is a bottom-up stock picker with a significant tilt towards smaller and mid-cap companies.
John Owen, chairman of the Fidelity China Special Situations fund, said: "Stepping into the shoes of Anthony is a significant challenge so we are delighted to have appointed a portfolio manager with a demonstrable record of success investing in the Asia Pacific region and specifically within China.
"We have selected Dale to continue the research-driven stock-picking approach which we continue to believe is the route to success in this exciting market."
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Jackie Beard, director of closed-end fund research at Morningstar said: "The news that Anthony Bolton has confirmed his intention to step down from fund management in April 2014 has not come as a surprise. The fund's performance this year has been markedly better than the first two years and Bolton wanted a good end to a long and successful career.
"We welcome the clarity that investors now have regarding the fund's future management. Dale Nicholls is a long-standing Fidelity employee who has a bent towards smaller companies. He uses the same analytical resources that Bolton himself draws upon and he has been running funds for Fidelity in the Asian region for almost a decade."
She said that Morningstar had put the fund under review.
Mark Dampier, head of investment research at Hargreaves Lansdown, said: "Anthony has had a fantastic career; he is rightly regarded as one of the best active managers of recent decades. His China fund's performance in recent years has tarnished this record slightly, though it has shown signs of recovery in the past year."

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