Earlier, Iran had warned Samsung of "repercussions" after the snub.
Iran on Thursday had summoned South Korea's Ambassador to the country over reports that its athletes would not each receive the 1,100 dollars smartphone.
However, the International Olympic Committee decided that the phones could not be given to Iranian and North Korean athletes due to United Nations sanctions imposed on the two countries.
The IOC had announced earlier Friday that it has made a decision to allow athletes from Iran and North Korea to receive the Olympic edition of the Samsung Galaxy Note8 after the Iranian government summoned the South Korean envoy to Tehran to lodge a formal complaint.
Also, Iran's Prosecutor General Mohammad Jafar Montazeri ordered his deputy to summon Samsung representatives in Tehran to protest at the Pyeongchang Winter Olympics organizers' move against Iranian athletes.
"A letter was today sent from Pyeongchang 2018 President Mr Lee Hee-beom.to apologise for the misunderstanding regarding the distribution of mobile phones to the Iranian athletes", a statement from Pyeongchang 2018 said.
"Through their apology and admission of their mistake, we have reached our goal and the offence against the Islamic Republic's athletes and nation has been rectified", the state news agency IRNA quoted Soltanifar as saying.
Samsung, an official worldwide partner of the Games, had prepared some 4,000 Olympic editions of the Galaxy Note8 phone to give to participating athletes as well as IOC staff.
In a press release to the Tehran Times, the ambassador said, "The Embassy of the Republic of Korea confirms that the unwise decision yesterday (Feb. 7) did come from neither the Korean government nor the Korean company in question".
Although the organisers later backtracked, it sparked anger in Iran, where Samsung has a major commercial presence, and its athletes refused to accept the phones until there was a full apology.
"Regarding North Korea, all participants are requested not to take the phones back to their home country but to only use them during their stay in PyeongChang, since that is required to allow them to participate in the Games", the International Olympic Committee said.
The Pyeongchang 2018 Olympic Games limited edition handset includes the bold new features of the Galaxy Note8, such as the innovative bezel-less 6.3-inch infinity display that the company claims fits comfortably in one hand, enhanced S pen for efficient productivity, and Samsung's best-in-class dual camera.
The phone also features celebratory pre-loaded Pyeongchang 2018 themed wallpapers, allowing recipients to stay connected through Samsung's most advanced mobile technology.
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