The Android handset hit the milestone ahead of schedule, having been forecast to reach the figure by the end of July.
J K Shin, head of Samsung's mobile communications division, told the Yonhap news agency: "It appears that it [accumulated sales] has exceeded 10 million units."
The flagship smartphone launched at the end of May, and is now available in 140 countries. Samsung predicts that the device will surpass 19 million sales by the autumn.
The Samsung Galaxy S3, featuring a 4.8-inch screen and fast quad-core processor, became the fastest-selling pre-order phone of all time following its unveiling, with reports suggesting that it attracted more than 9m advance purchases.
The Korean tech giant confirmed at the beginning of June that combined shipment figures for its Galaxy range have exceeded 50 million units.
The Galaxy S3 is expected to face stiff competition from Apple's iPhone 5, which has been rumoured for release in September or October.
Watch a video introducing the Samsung Galaxy S3 below: