Hazrat Umar (Radiyallahu Anhu) used to make the following Dua:

اللَّهُمَّ ارْزُقْنِي شَهَادَةً فِي سَبِيلِكَ، وَاجْعَلْ مَوْتِي فِي بَلَدِ رَسُولِكَ صَلَّى اللهُ عَلَيْهِ وَسَلَّمَ

“O Allah bless me with martyrdom in Your path and make my death in the city of Your Rasool (ﷺ)” (Bukhari #1890)

Hazrat Umar (Radiyallahu Anha) had seen a dream where a rooster had pecked him three times. He suspected that this was indicating towards his death. He sought the interpretation of this dream from Hazrat Asma bint Umais (Radiyallahu Anha), the wife of Hazrat Ali (Radiyallahu Anhu), and she confirmed the same.
A Persian Abu Lulu Fayrooz, who was the slave of Hazrat Mugheerah ibn Shu’bah (Radiyallahu Anhu) attacked him and he passed away on the 1st Muharram 24 A.H. He was buried in the Rowdha Aqdas of Rasulullah (ﷺ).

The incident regarding his martyrdom is that one morning he left home for Fajr Salah carrying his whip in his hand. He would straighten the Saffs using his whip. After the Iqamah was called out, he raised his hands to say the Takbeer when Abu Lulu pounced on him and stabbed him with a dagger in his stomach. Hazrat Umar (Radiyallahu anhu) fell unconscious and Hazrat Abdur Rahman ibn Auf (Radiyallahu Anhu) stepped forward to complete the Salah. Abu Lulu tried to escape through the Saffs of the Musallis but was unable to do so. Some of the Musallis caught him. He had stabbed 13 other Sahabah (Radiyallahu Anhum). Seven of them had also passed away.

When he realised he was caught, he killed himself with the same dagger. After the Salah was over, Hazrat Umar (Radiyallahu Anhu) was rushed to his home. This incident took place on Wednesday, 27th Zul Hijjah 23 A.H. Medical treatment was administered to him but were not able to heal his wounds.

Before this, Abu Lulu had come to Hazrat Umar (Radiyallahu Anhu) to complain regarding Hazrat Mughirah ibn Shu’bah (Radiyallahu Anhu) that he was burdening him with too much. Hazrat Umar (Radiyallahu Anhu) asked him what work he does etc. When he told him that he makes grinding mills etc., Hazrat Umar (Radiyallahu Anhu) told him to continue but also had the intention of asking Hazrat Mughirah ibn Shu’bah (Radiyallahu Anhu) to lessen his burden. Abu Lulu wasn’t happy and made his intention at that time to kill Hazrat Umar (Radiyallahu Anhu). He indicated towards this when Hazrat Umar (Radiyallahu Anhu) asked him if he could make a grinding mill for him also. He replied that he will make a special one for him. Hazrat Umar (Radiyallahu Anhu) then asked Hazrat Ali (Radiyallahu Anhu) who was with him, “What do you think he means?” Hazrat Ali (Radiyallahu Anhu) replied, “He has promised you (to kill you) o Ameerul Mu’mineen.” Hazrat Umar (Radiayllahu Anhu) replied, “May Allah suffice me against him …”

On the night that Hazrat Umar (Radiyallahu Anhu) was stabbed, Hazrat Miswar bin Makhramah (Radiyallahu Anhu) came to see him. On entering, he found Hazrat Umar (Radhiyallahu Anhu) covered with a sheet (and unconscious). Miswar (Radiyallahu Anhu) asked those present, “How is he?” They replied, “He is as you can see (unconscious).”

Miswar (Radiyallahu Anhu) thus advised them, “Wake him up by calling him for Salah, as there is nothing that you can awaken him for that is more urgent and important to him than Salah.” Accepting this suggestion, they called out, “Salah, O Ameerul Mu-mineen!” As soon as they did this, Hazrat Umar (Radiyallahu Anhu) awoke and exclaimed, “Yes! By Allah! There is no share in Islam for the one who neglects Salah!” Hazrat Umar (Radiyallahu Anhu) thereafter performed his Salah while blood flowed from his wound. (Tabraani – Majma‘uz Zawaaid #1659)
He asked, “Who was my murderer?” He was told it was Abu Lulu Majoosi. He thanked Allah that he was martyred by a non-Muslim

During this period, a youngster visited Hazrat Umar (Radiyallahu Anhu) and said, “O Ameerul Mumineen! Rejoice over glad tidings from Allah! You are the Sahabi of Rasulullah (ﷺ), you accepted Islam in the very early stages, you were thereafter appointed as the Khalifah and exercised justice, and you will shortly pass away a martyr!”
When he heard this, Hazrat Umar (Radiyallahu Anhu) remarked, “I wish that all these aspects (that you have mentioned, and all my good deeds) assist me to just break even (i.e. I would be happy if all my good deeds are merely sufficient to counter-balance my evil sins), so that there is nothing against me, (even if there are) and no deeds in my favour.”

When this youngster turned to leave, Hazrat Umar (Radiyallahu Anhu) noticed his lower garment (below his ankles) touching the ground. Hazrat Umar (Radiyallahu Anhu) immediately ordered for him to be brought back, after which he told him, “O nephew! Raise your lower garment, for it is cleaner for your clothing and a means of adopting fear of Allah Ta‘ala.” (Bukhari #3700)

In this time he asked his son Hazrat Abdullah (Radiyallahu Anhu) to see how much his debts were. They totalled approximately 86000. (This was what he had taken from the Baitul Maal as remuneration).

Abul Matar narrates, ‘I heard Hazrat Ali (Radiyallahu Anhu) saying, “I visited Hazrat Umar bin Khattab (Radiyallahu Anhu) after Abu Lulu had stabbed him and he was crying. So I said to him, “What makes you cry O Ameerul Mu’mineen?” He replied, “The information of the sky makes me cry. Will it take me to Jannah or the Fire (of Jahannam)?” So I said to him, “Take glad tidings of Jannah, because I heard Rasulullah (ﷺ) say innumerable times, “The leaders of the elderly people of Jannah will be Abu Bakr and Umar.” So he asked, “Are you a witness for me that I will be in Jannah? “So I replied, “Yes. And you O Hasan be a witness upon your grandfather Rasulullah (ﷺ) that Umar is from the people of Jannah.” (Tareekh Dimishq Vol.44 Pg.168)

When the Sahabah realised that there was no chance for his survival, they were overcome with extreme grief and sorrow. Hazrat Umar (Radiyallahu Anhu) told his son Abdullah, “Go to Hazrat Ayesha (Radiyallahu Anha) and say Umar conveys Salaams to her. Do not say Ameerul Mu’mineen because I am no longer the Ameerul Mu’mineen. Say Umar ibn Khattab requests permission to be buried alongside his two companions (Rasulullah ﷺ and Hazrat Abu Bakr Siddeeq Radiyallahu Anhu).” So Hazrat Abdullah ibn Umar (Radiyallahu Anhuma) went to Hazrat Ayesha (Radiyallahu Anha), made salaam and sought permission to enter. Then he entered and found her sitting and crying. So he said, “Umar ibn Khattab conveys Salaams to you and requests permission to be buried with his two companions.”

When Hazrat Ayesha (Radiyallahu Anha) heard this, she said, “I had reserved this place for me, but I shall give preference to him over myself.”

Then he returned to Hazrat Umar (Radiyalahu Anhu). Hazrat Umar (Radiyallahu Anhu) asked him what information he had. He replied, “What you have desired O Ameerul Mu’mineen. You have been given permission.” He replied, “Alhamdulillah! Nothing is more beloved to me than that. When I die then carry me there, make Salaam then say, “Umar ibn Khattab requests permission. If she grants permission then take me inside. If she rejects me return me to the Qabrastan (Jannatul Baqi) of the Muslims. That is better for me.” (Bukhari #3700)

At the time of his demise his head was resting on the thigh of his son Hazrat Abdullah ibn Umar (Radiyallahu Anhuma). In these last moments he said, “Put my head on the ground.” Although his son said that there was nothing wrong in having his head on his (Abdullah’s) thigh, Hazrat Umar (Radiyallahu Anhu) insisted that his head be put on the ground. After this was done, he said,

وَيْلٌ لِي وَلِأُمِّي إِنْ لَمْ يَرْحَمْنِيْ لِي رَبِّي

“Destruction for and my mother if My Rabb does not have mercy on me.”

Thereafter Hazrat Umar (Radiyallahu Anhu) began experiencing the pangs of death. He passed away on 1st Muharram 24 A.H. on Sunday. (Inna Lillahi Wa Inna Ilaihi Rajioon). He also passed away at the age of 63 like Rasulullah (ﷺ) and Hazrat Abu Bakr (Radiyallahu Anhu).
When he passed away then they went walking with him to the house of Hazrat Ayesha (Radiyallahu Anha). Hazrat Abdullah ibn Umar (Radiyallahu Anhuma) made salaam and said, “Umar seeks permission.” Hazrat Ayesha (Radiyallahu Anha) replied, “Bring him in.” So he was brought in and placed him with his 2 companions. (Bukhari #3700)

Hazrat Ayesha (Radiyallahu Anha) says, “I would enter my room in which Rasulullah (ﷺ) and my father (Hazrat Abu Bakr Radiyallahu Anhu) were buried without being properly covered because it was just my husband and my father. However, after Hazrat Umar (Radiyallahu Anhu) was buried there with them, by Allah, I would never enter the room without being properly covered out of Hayaa (modesty/shame) for Hazrat Umar (Radiyallahu Anhu). (Musnad Ahmad #25660, Mustadrak Lil Hakim #4460, Majmauz Zawaaid #12704, #14274, Mishkat #1771)
Hazrat Suhaib Roomi (Radiyallahu Anhu) performed his Janazah Salah.

Abu Mulaikah narrates that he heard Hazrat Abdullah ibn Abbas (Radiyallahu Anhuma) saying, “Hazrat Umar (Radiyallahu Anhu) was placed on the bier. People surrounded him making Dua for him before the body was picked up. I was also among them. No one caught my attention except one person who was leaning over my shoulder. It was Hazrat Ali (Radiyallahu Anhu). He made Dua for the mercy of Allah to be on Hazrat Umar (Radiyallahu Anhu) and then said, “You have not left behind anyone that I desire to meet Allah with the likeness of his actions more than you. By Allah! I used to think that Allah will join you up with your two companions (Rasulullah ﷺ and Hazrat Abu Bakr Radiyallahu Anhu). I heard Rasulullah (ﷺ) saying many times, “I, Abu Bakr and Umar went (to a certain place). I, Abu Bakr and Umar entered (certain place). I, Abu Bakr and Umar came out (from a certain place).” (Bukhari #3685)