Darling, now a member of the House of Lords, was chancellor between 2007 and 2010 and served as a Labour MP for 28 years.
The 62-year-old has been a prominent member of the campaign backing Britain to remain within the EU.
Morgan Stanley chairman James Gorman said Darling's experience at the helm during the economic crash will be useful.
He said: "I am very pleased to welcome Darling to our Board. He brings strong leadership experience, as well as insight into both the global economy and the global financial system.
"As chancellor of the exchequer he played a central role in responding to the financial crisis. the board, our management and our shareholders will greatly benefit from his experience and perspective."
James W Owens, chairman of the board's nominating and governance committee, said: "We will all benefit from his financial, risk management and regulatory insights."