Yes, that is the punishment.
‘Umar ibn al-Khattaab (may Allaah be pleased with him) said, when he was sitting on the minbar of the Messenger of Allaah (peace and blessings of Allaah be upon him): “Allaah sent Muhammad (peace and blessings of Allaah be upon him) with the truth, and revealed to him the Book. One of the things that He revealed was the verse of stoning, which we have read and understood. The Messenger of Allaah (peace and blessings of Allaah be upon him) carried out the punishment of stoning and we did so after him. I fear that as time goes by, people will say, ‘We do not find any mention of stoning in the Book of Allaah,’ so they will go astray by forsaking an obligation that was revealed by Allaah. In the Book of Allaah, stoning is the punishment deserved by any previously-married person, man or woman, who commits adultery, if proof is established, or pregnancy results, or he or she confesses.”
(Narrated by al-Bukhaari, 2462; Muslim, 1691)
Please note that although the punishment is severe, the requirements that must be meet before anyone can be stoned to death are very strict:
Zina can only be proven by the testimony of four men who see the act take place with their own eyes, and see the male private part enter the female private part, or by the unforced confession of the man or woman who committed zina.
http://www.islam-qa.com/index.php?ref=8980&ln=eng
(I edited that a little to make it less explicit, and zina means adultery).
And obvious the adulters can only be sentences by relevant authority.
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