The British bank paid the American Express Company $823 million for AEB, which is its international banking subsidiary.
StanChart's chief executive, Peter Sands, said the takeover "brings along an exceptional management team".
AEB was established in 1919 and provides private banking services in 47 countries.
Although StanChart currently has good private banking business links with Asia, Africa and the Middle East, the acquisition should help it strengthen these, particularly in Singapore, Hong Kong and India.
New York, Miami, Geneva, Monaco, and London should all see an increase in business for StanChart through AEB, Xinhua notes.
StanChart will also benefit by doubling its US dollar clearing business as well as giving it clearing capabilities for the euro and the yen.
American Express has reportedly entered into a put and call arrangement with StanChart, which means the British bank has an option of buying American Express International Deposit Company in a year-and-a-half.