Mr Bonham Carter, who has been chief executive for 14 years, will move to a new role as vice chairman of the London-based fund manager.
He will remain on the board, reporting to Mr Slendebroek.
A statement from Jupiter today said: "The board of Jupiter Fund Management announces that Maarten Slendebroek will succeed Edward Bonham Carter as group chief executive with effect from 17 March 2014."
Mr Bonham Carter said: "It has been a privilege to lead Jupiter during the past 14 years. The company is well positioned for growth and it is the right time for me to hand over the reins.
"I have enjoyed working with Maarten since his arrival and he has the skills and qualities to take the company through the next stage of its growth. I look forward to helping the team execute Jupiter's strategy in my new role."
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Mr Slendebroek said: "Jupiter is a great business with a strong brand and culture, and a record of investment outperformance. We have been gaining traction with a broader range of clients in the UK and internationally in recent years and I am delighted to have the opportunity to build this growth strategy out further, working with my colleagues in order to deliver value for our clients and shareholders."
Jupiter has grown strongly in recent years and Jamie Dundas, Jupiter chairman, said that Mr Bonham Carter had left the company in good shape.
He added: "Maarten takes over from Edward with Jupiter in excellent shape, with strong performance, record assets under management and a robust balance sheet.
"Maarten has made a significant contribution since he joined the company as distribution and strategy director and his appointment as group chief executive is a natural evolution of Jupiter's executive team.
"I am also delighted that Edward, who has achieved so much for Jupiter, will stay with us in a new executive role focusing on engaging with key stakeholders - an increasingly important requirement as we grow."
Jupiter has a wide range of retail funds and is popular with intermediaries. Funds are mostly actively manager and include Jupiter Financial Opportunities and Jupiter European.