He is leaving to “establish a portfolio of private equity opportunities” and will be succeeded by Andy Parker, current deputy chief executive.
Shares in Capita fell as much as 5pc in early trading on Monday before easing back to trade down 1.3pc.
Mr Pindar said in a statement: “After 26 years with the company and approaching my 50th results presentation, I believe that now is the right time to hand the reins over to Andy.
“I will be leaving Capita with a strong management team and in excellent financial and operational shape for further success in 2014 and beyond.”
Mr Pindar, a chartered accountant, joined Capita in 1987 from private equity group 3i, after advising Capita on its management buy-out. He became chief executive in 1999.
His replacement Alan Parker joined the group in 2001 and was appointed to the board as joint chief operating officer in January 2011.
Capita has largely avoided the problems of rival outsourcing companies G4S and Serco, which are facing a Serious Fraud Office investigation over alleged breaches of government contracts and claims they overcharged for tagging criminals.
Analysts at Investec said: “Paul Pindar … has been pivotal not only in managing the group through its exceptional growth phase, but also in steering it through more challenging times recently. Today’s departure, alongside uncertainty around the support of its largest shareholder may well see the shares come under some near term pressure.”
Investec added: “The group is firmly on track to deliver its previously stated 8pc organic revenue growth target, with the operating margin set to be comfortably within its stated range of 12.5pc-13.5pc. Cash conversion is also strong, with the conversion rate of operating profit to operating cash in excess of 100pc.”