Hadith: As the verse of Hajj Tamattu‘ was revealed, the Messenger (may Allah's peace and blessings be upon him) ordered us to perform it. Nothing was revealed in the Qur'an abrogating it nor did the Prophet (may Allah's peace and blessings be upon him) prohibit it until he died

عن عمران بن حصين رضي الله عنهما قال: «أُنْزِلَت آيَةُ المُتْعَةِ في كتاب اللَّه تعالى ، فَفَعَلْنَاهَا مَعَ رَسُولِ اللَّهِ صلى الله عليه وسلم ، وَلَم يَنْزِلْ قُرْآنٌ يُحَرِّمُهَا، وَلَم يَنْهَ عَنهَا حَتَّى مات، قال رجل بِرَأْيِهِ مَا شَاءَ»، قال البخاري: «يقال إنه عمر». وفي رواية: « نَزَلَت آيَةُ المُتْعَةِ -يَعْنِي مُتْعَةَ الحَجِّ- وَأَمَرَنا بِهَا رَسُولُ اللَّهِ صلى الله عليه وسلم ، ثُمَّ لَم تَنْزِل آيَةٌ تَنْسَخُ آيَةَ مُتْعَةِ الْحَجِّ، وَلَمْ يَنْهَ عَنْهَا رَسُولُ اللَّهِ صلى الله عليه وسلم حَتَّى مَاتَ». ولهما بمعناه.
[صحيح] - [الرواية الأولى: متفق عليها. الرواية الثانية: رواها مسلم]

‘Imrān ibn Husayn (may Allah be pleased with him) reported: The verse of Hajj Tamattu‘ was revealed in Allah's Book. We performed it with the Messenger (may Allah's peace and blessings be upon him) and nothing was revealed in Qur'an to make it unlawful, nor did the Prophet prohibit it till he died. No regard is therefore given to anyone suggesting otherwise. Al-Bukhāri said: "It was said that man is ‘Umar." In another narration: "As the verse of Hajj Tamattu‘ was revealed, the Messenger (may Allah's peace and blessings be upon him) ordered us to perform it. Nothing was revealed in the Qur'an abrogating it, nor did the Prophet (may Allah's peace and blessings be upon him) prohibit it till he died." And they both narrated it with this meaning.
[Authentic hadith] - [Narrated by Muslim - Narrated by Bukhari & Muslim]

Explanation

‘Imrān ibn Husayn (may Allah be pleased with him) says that Hajj Tamattu‘ was laid down in the Qur'an and the Sunnah. In the Qur'an, Allah, the Almighty, says: {And whosoever performs the 'Umrah in the months of Hajj, before (performing) the Hajj, he must slaughter a Hady such as he can afford} [Sūrat al-Baqarah: 196]. As for its legislation in the Sunnah, this is represented by the Prophet's performance and approval of this act, whereas no Qur'anic verses were revealed to prohibit it, nor did the Prophet forbade it later, till he died. So, ‘Imrān wonders: How can anybody prohibit it after that! By this, he refers to ‘Umar ibn al-Khattāb, who prohibited Hajj Tamattu‘, based on his own reasoning, aimed at boosts the pilgrims' numbers throughout the year. If a pilgrim performs ‘Umrah along with Hajj, he or she will only come during the season of Hajj. So, ‘Umar's ban was not meant as prohibition or abandonment of the application of the Qur'an and Sunnah in this respect; rather, it was a temporary ban for the public interest.