The Silicon Valley venture capitalist's firm Khosla Ventures is an early investor in Square.
Khosla will be replacing Gideon Yu, Facebook's former chief financial officer.
Yu recently left the company's board and Khosla Ventures to join the professional football team San Francisco 49ers as Chief Strategy Officer.
"Square is thrilled to welcome Vinod to our board. We have worked closely with Khosla Ventures since our inception and Vinod's expertise, history and input will be a tremendous asset to our company as we continue to grow," Square CEO Dorsey said in a statement.
In 2009, Khosla Ventures led Square's initial venture round queueing up the company for its launch, and participated in Square's Series B round in January 2011, the mobile payment firm said.
The IIT-Delhi alumnus co-founded Sun Microsystems in 1982.
He went on to become a general partner at Kleiner Perkins and then founded his own venture fund Khosla Ventures in 2004.
Khosla currently manages more than USD 1 billion in investor money. His firm focuses on clean technologies and information technologies.
Square, which recently received new strategic investment from Visa, achieved a target of processing USD 3 million in payments per day.
The company aims to process USD 1 billion in payment volume within a year.
