State media in the gas-rich Gulf state said Emir Sheikh Tamim bin Hamad Al-Thani had sent a cable of congratulations to the Saudi leadership.
The message was sent to King Salman "on the occasion of the selection of his royal highness Prince Mohammed bin Salman bin Abdulaziz Al-Saud as Crown Prince", said the Qatar News Agency.
The statement also expressed hopes "brotherly relations between the two brotherly countries".
A message of congratulations was also posted on social media.
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As well as diplomatic isolation, other measures taken included the closing of Qatar's only land border, which it shares with Saudi.
Qatar denies the charges of supporting extremism.
Despite efforts at mediation from Kuwait, Turkey and the United States, the dispute between the Gulf countries has now entered its third week.