The talbiyah of the Messenger of Allah ﷺ was, "Here I am, O Allah, here I am. Here I am, You have no partner, here I am. Indeed, all praise, blessings, and dominion belong to You. You have no partner."The narrator said that Abdullah bin Umar used to add to it, "Here I am, here I am. Here I am, ready to obey You. All good is in Your hands. Here I am. To You is all longing, and to You belongs every deed."
أن تلبية رسول الله ﷺ: لبيك اللهم لبيك، لبيك لا شريك لك لبيك، إن الحمد والنعمة لك والملك، لا شريك لك. قال: وكان عبد الله بن عمر يزيد فيها: لبيك لبيك، لبيك وسعديك، والخير بيديك، لبيك والرغباء إليك والعمل.
Malik narrated it in the Hajj chapter (28) from Nafi, from Ibn Umar, as mentioned above. Bukhari narrated it in the Hajj chapter (1549), and Muslim in the Hajj chapter (1184:19), both by way of Malik, with the same wording, except that Bukhari did not mention Ibn Umar's talbiyah.Bukhari also narrated it in the chapter on clothing (5915), and Muslim in the Hajj chapter (1184:21), both by way of Abdullah bin Wahb, who said, Yunus informed me, from Ibn Shihab Zuhri, that Salim bin Abdullah bin Umar informed him, from his father, who said, "I heard the Messenger of Allah ﷺ raise his voice in the talbiyah with matted hair, saying" (then he mentioned the talbiyah of the Messenger of Allah ﷺ as in the report of Malik), then he said, "He would not add anything beyond these words."Muslim added, "And Abdullah bin Umar used to say, Umar bin Khattab used to perform the talbiyah with the same words as the talbiyah of the Messenger of Allah ﷺ, and he would say, 'Here I am at Your service, O Allah, here I am. Here I am at Your service, You have no partner, all good is in Your hands, here I am. All desire is directed to You, and so is all deed.'"Tirmidhi (826) said, following the hadith of Ibn Umar, "The hadith of Ibn Umar is a hasan sahih hadith, and this is the practice followed by some of the scholars among the companions of the Prophet ﷺ and others, and it is the view of Sufyan, Shafii, Ahmad, and Ishaq. Shafii said, If one adds something to the talbiyah by way of glorifying Allah, there is no harm in it, Allah willing, but I prefer that one confine himself to the talbiyah of the Messenger of Allah ﷺ." End of quote.As for the additions that Ibn Umar added, the correct view is that they were additions made by his father, and that he was simply following his father's example in that.