Ajay Sharma will lead Obi Mobiles as CEO. Sharma was previously associated with Micromax and HTC as their smartphone division head.
Sculley served as chief executive of Apple from 1983 to 1993.
Inflexionpoint plans to set up a supply chain, design centre and offices in India, producing affordable smartphones that will not lack of high-end features, according to Sculley.
The company also aims to expand to other growing markets in the Asia-Pacific, Middle East and Latin America.