As well as serving both presidents Clinton and Obama, Summers is a former president of Harvard. He joins venture capitalist and Sun Microsystems co-founder Vinod Khosla who also recently joined the Square board.

Led by Twitter co-founder Jack Dorsey, Square provides merchants with a piece of plastic that fits in to the headphone jack of handsets and acts as a card swipe for processing payments.

According to some press reports, the fast-growing firm is currently putting together a $50 million funding round that would give it a $2 billion valuation.

Says Dorsey: "Square is at a key point in our trajectory and we know Larry will contribute tremendous wisdom and expertise toward our continued success."