Boston-based Strategy Analytics said 18 million S IIIs were sold in the third quarter of this year, knocking Apple off the top spot for the first time in two years.
In contrast, Apple sold 16.2 million of its iPhone 4S devices.
But this was partly due to prospective buyers waiting for its successor, the iPhone 5, which launched toward the end of the quarter on September 21.
Strong sales of the flagship Galaxy S III, which comes with a large 4.8in touchscreen, helped Samsung post a record £4.6bn ($7.3bn) operating profit in the July-September quarter.
The iPhone 5 sold an estimated six million units in just nine days at the end of the third quarter, which ended on September 30.
Despite the success of the iPhone 5 and its high hopes for the iPad mini, Apple's shares have been in decline.
They were $549.38 (£343.82) on Thursday compared with more than $700 (£438.08) two months ago.
Last month Apple posted quarterly earnings that were below Wall Street's expectations.
Apple missed analysts' forecasts for the second straight quarter after sales of iPads failed to please.
More From Sky News