The devices were recalled due to overheating or catching fire issues.
The company said that over 60% of all recalled Galaxy Note 7 phones sold in the US and Korea have been exchanged through the programme.
Earlier this month, Samsung issued a voluntary recall for its Galaxy Note7 devices after facing overheating or catching fire issues in 35 cases.
Samsung mobile communications business DJ Koh said: “Just over three weeks ago, Samsung committed to a global replacement program for the Galaxy Note7. Last week, that program began for the majority of markets and the progress is encouraging.
“Our focus now is to make sure that all affected devices are replaced as quickly and efficiently as possible.”
The company said that nearly 90% of Galaxy Note 7 users have been going for a new Galaxy Note 7 since products became widely available.
In Singapore, the exchange programme, which began on 17 September, saw participation from over 80% of the company’s customers.
Koh said: “This is why we want them to take advantage of their local replacement program so that they can continue to feel confident and excited every time they reach for their Galaxy Note7 device.”
Samsung said that it is working with national regulatory bodies as part of efforts to address the issues.
Following reports of devices catching fire, the US authorities had warned airline passengers not to turn on or charge their Samsung Galaxy Note 7 phones when on board a plane.
The company reiterated that customers owing affected Galaxy Note 7 devices should switch off them and return their devices for replacement.
Earlier, the smartphone-maker said that it would a software update for its Galaxy Note 7 customers in South Korea as part of efforts to address overheating concerns.
The software update was aimed at limiting the battery’s capacity of the smartphone at 60% to prevent overheating.
In August, Samsung unveiled the Galaxy Note 7, which updates its flagship phablet line with new durability and security features.
The smartphone features a new iris scanner to boost the security of the device. The company developed its own proprietary algorithm to assign a digital signature to each user’s iris.