"The exchange programme began today (Monday) and is being carried out without problems," a spokesperson of the company, headquartered in Seoul, told EFE news.
Note 7 users who had returned their old devices will receive a new smartphone of the same model and colour unless they opt for a refund.
In South Korea, the exchange is taking place 17 days after the company announced the recall and will take place in other parts of the world in the coming days -- except Canada and Singapore where the company began handing out the new devices last week.
The new Galaxy Note 7 has a green battery indicator that separates it from the earlier version.
Of the 2.5 million Note 7 sold worldwide since its launch on August 19, around 400,000 were sold in South Korea and one million in the US.
Samsung recalled Note 7 on September 2 after admitting that in 35 cases the devices had caught fire while they were being charged owing to faulty batteries.
A fortnight later, on September 16, the US Consumer Product Safety Commission ordered Samsung to recall the devices due to a risk they could overheat or explode.