Sikka, 47, who was previously executive board member of German IT firm SAP, will replace S D Shibulal, one of the seven engineers who founded Infosys in 1981, from August 1, Infosys said in a statement.
Along with Murthy, who upon return from retirement in June last year wanted five years as chairman to turn around the sagging fortunes of Infosys, Executive Vice Chairman S Gopalakrishnan will also step down on June 14.
Murthy will be replaced veteran banker K V Kamath as non-executive Chairman of the Infosys board.
Infosys said the chairman's office would be dissolved and Rohan, who was brought in by his father as his executive assistant last year, would leave the company on Saturday, when the annual shareholders meeting is held in Bangalore.
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Murthy will be designated chairman emeritus from October 11, the day Kamath will assume the role of non-executive chairman.
Sikka, who quit SAP in May, comes in after four straight years of narrowing margins at Infosys. He will also be the company's managing director.
The Infosys scrip fell 0.38 per cent to Rs 3,166.60 at the close on the BSE, after the day's high of Rs 3,298.