Mr Darling, who served as the Chancellor of the Exchequer from 2007 to 2010, will take up the role in January.
His move follows former Prime Minister Gordon Brown's appointment to an advisory panel at the global investment firm Pimco.
Mr Darling, 62, played a key role in addressing the global economic crisis.
Morgan Stanley's chief executive James Gorman said the US bank would "greatly benefit from his experience."
"He brings strong leadership experience, as well as insight into both the global economy and the global financial system," said Mr Gorman.
In 2014 members of Morgan Stanley's board of directors received $75,000 (£49,960) a year plus an additional $10,000 to $30,000 for leading or joining a committee within the board. Each board member also received $250,000 in stock awards.
On Monday Mr Brown, who served as Prime Minister when Mr Darling was chancellor, joined Pimco's five-strong group of "world-renowned experts on economic and political issues".
The other members include former US Federal Reserve chairman Ben Bernanke, and Jean-Claude Trichet, former president of the European Central Bank.
A spokesman for Mr Brown said he was taking on "a minor advisory role" and would not financially benefit.
The spokesman added: "Any money goes to the office of Gordon and Sarah Brown to support their charitable and public service work."
