Yes, this hadeeth is authentic. This hadeeth occurs in the Saheeh of al-Bukhaaree, in "Kitaab ul-Ahkaam" under the chapter of "Istikhlaaf":
حَدَّثَنِي مُحَمَّدُ بْنُ الْمُثَنَّى حَدَّثَنَا غُنْدَرٌ حَدَّثَنَا
شُعْبَةُ عَنْ عَبْدِ الْمَلِكِ سَمِعْتُ جَابِرَ بْنَ سَمُرَةَ قَالَ
سَمِعْتُ النَّبِيَّ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ يَقُولُ يَكُونُ
اثْنَا عَشَرَ أَمِيرًا فَقَالَ كَلِمَةً لَمْ أَسْمَعْهَا فَقَالَ أَبِي
إِنَّهُ قَالَ كُلُّهُمْ مِنْ قُرَيْشٍ
From Jaabir bin Samurah who said:
I heard the Prophet (sallallaahu alayhi wasallam) say: "There will be twelve ameers (leaders)", and then he said a word that I did not hear. Then he said: Meaning, he (the Prophet) said: "All of them are from Quraish."
There are two Sunni views that I would like to present. One that is of Ibn Katheer as discussed in his tafseer and another of Shaykh Abdul-Aziz ibn Abdullah ibn Baz (May Allah have mercy on him).
The view of Ibn Katheer:
Ibn Katheer discusses this matter in his tafseer of the verse in Surah al-Maa'idah (5:12), which mentions twelve elders raised amongst Banee Israa'eel (I quote only parts of it):
And the basis of this hadeeth is established in the two Saheehs from
the hadeeth of Jaabir bin Samurah who said:
I heard the Prophet (sallallaahu alayhi wasallam) saying: "The affair
of the people will never cease to continue so long as twelve men take
authority over them." Then the Prophet (sallallaahu alayhi wasallam)
spoke with a word which was not audible to me, so I asked, meaning
"What?" The Prophet (sallallaahu alayhi wasallam) said, "All of them
are from Quraish."
And this is the wording of Muslim.
And the meaning of this hadeeth is the glad tiding of the presence of
twelve righteous khalifahs who will establish the truth and rule with
justice over them [the people]. And it is not binding from this that
their rule be successive, following each other [in succession].
Rather, four of them have already been found in order, and they are
the four rightly guided khalifahs: Abu Bakr, Umar, Uthmaan and Alee
(radiallaahu anhum), and amongst them is Umar bin Abdul-Azeez without
doubt in the view of the Scholars. And after the Banee al-Abbaas, the
Hour will not be established until their rule (i.e those who remain
from the twelve) has taken place, certainly. And what is apparent is
that the promised Mahdi [mentioned] in the reported ahaadeeth is from
amongst them. So it has been mentioned that his name will concur
with the name of the Prophet (sallallaahu alayhi wasallam) and that
the name of his father will be the name of his (the Prophet's) father,
and that he will fill the earth with justice, just as it had been
filled with tyranny and oppression.
View of Shaykh Ibn Baaz:
Shaykh Ibn Baaz (rahimahullaah) has a view different to that of Ibn Katheer on this subject, regarding the specification of these twelve rulers. He states (Majmoo' Fataawaa 4/99-101):
There are some of the scholars who gave some irregular opinions in
this regard but their views are not considered here. As for what
Al-Hafiz Isma'il ibn Kathir (may Allah confer His Mercy on him) stated
in his book of the exegesis of the Qur'an in Surah of Al-Ma'idah while
speaking about the deputies of the people of Medina, that Al-Mahdi may
be one of The Twelve Imams, this is doubtful.
The Prophet (may Allah's Peace and Blessings be upon him) said: "The
matter of this nation will continue well-established when they are
ruled by twelve caliphs who all belong to Quraysh".
The saying of the Prophet (peace be upon him) indicates that religion
at their time is established and prevailing and the truth is apparent.
It is known that this prophecy was fulfilled before the end of the
era of Banu Umayyah. However, during the last days of this era a
great difference occurred which caused disunity and was a disaster for
Muslims for they divided into two countries, one in Andalusia and one
in Iraq as well as other inflictions which affected Muslims during
this time as known.
The Prophet (peace be upon him) said: "The matter of this nation will
continue well-established..." Then, there were many great matters that
helped unbalance the system of caliphate and the Islamic territory
disunited into small countries with their own rulers, as is the case
in the present time, even widely and apparently.
To this day, Al-Mahdi has not appeared so how can one dare to say that
the matter of religion will continue well-established until the coming
of Al-Mahdi? Indeed, this is rejected by fair thinking and
According to some scholars, the most proper meaning of the Hadith,
"The matter of this nation will continue well-established when they
are ruled by twelve caliphs who all belong to Quraysh", is that the
Prophet (peace be upon him) intends the four caliphs (Abu Bakr,
Umar, Uthman, and Alee (radiallahu anhum)), Mu'awiyah (may Allah be
pleased with them), his son Yazid , 'Abdul-Malik ibn Marwan, his four
sons and 'Umar ibn 'Abdul-`Aziz. These are twelve caliphs.
What I want to assure is that the strongest and soundest view
concerning the twelve Imams is that they end with Hisham ibn
'Abdul-Malik as religion in their time was established, Islam was
prevailing, the truth was apparent and Jihad was in force. As for what
happened after the death of Yazid of difference and disunity in the
caliphate so that Marwan ruled Al-Sham (The Levant) and Ibn Al-Zubayr
ruled Hijaz all of this did not harm Muslims in their religion for
their religion was predominant and widespread and their enemy was
subjugated in spite of the dispute that happened then it ended by
paying the pledge of allegiance to to 'Abdul-Malik and people became
united in spite of the trouble that happened at the hands of Al-Hajjaj
It becomes clear that the matter which the Prophet (peace be upon him)
told us about has happened and ended whereas the matter of Al-Mahdi is
to be during the last days (of the world) and that it has no relation
to the Hadith narrated by Jabir ibn Samurah concerning the Twelve
Upon this view, four of the rulers were in the period of Prophetic khilaafah (Abu Bakr, Umar, Uthman and Alee (radiallahu anhum)) and the rest were in the period of kingship, and the reign of all of these twelve rulers (ameers, khalifahs) ended before the first century of Islaam, as Umar bin Abdul-Azeez died in 97H.
Source: Concerning the Twelve Khalifahs That Will Rule Before the Hour, All Of Them From the Quraish,
Speech of Ibn Baaz concerning this affair