There is no specific du’aa’ narrated in the Sunnah for after one has completed the Qur’aan, or even from the companions of the Prophet (peace and blessings of Allaah be upon him) or the well-known imams. One of the most well-known du’aa’s regarding this matter is the du’aa’ which is written at the end of many Mus-hafs and it attributed to Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him), but there is no basis for attributing it to him. See Fataawa al-Shaykh Ibn ‘Uthaymeen, 14/226. 

The du’aa’ after completing the Qur’aan is recited either after completing it whilst praying, or when not praying. There is no basis for reciting any du’aa’ after completing it whilst praying. As for reciting a du’aa’ after completing it when not praying, it is narrated that Anas (may Allaah be pleased with him) did that. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked: What is the ruling on making du’aa’ after completing the Qur’aan in night prayers in Ramadaan?  

He replied: 

I do not know of any du’aa’ for completing the Qur’aan in night prayers in Ramadaan, either from the Prophet (peace and blessings of Allaah be upon him) or from his companions. The most that has been narrated concerning that is that when Anas ibn Maalik (may Allaah have mercy on him) had completed a reading of the Qur’aan, he would gather his family and make du’aa’. This had to do with reading it outside of prayer. End quote. 

Fataawa Arkaan al-Islam, p. 354 

Shaykh Bakr Abu Zayd wrote a useful essay on this issue, at the end of which he said: 

From the quotations in the two previous sections we may draw the following conclusion: 

1 – Du’aa’ upon completion of the Qur’aan in general: 

The conclusion concerning this is as follows: 

Firstly: 

What we have stated above has to do with du’aa’ upon completion of the Qur’aan in general. 

There is no proof that the Prophet (peace and blessings of Allaah be upon him) did that, rather the reports are either mawdoo’ (fabricated) or are da’eef (weak) with no other reports to strengthen them. It is almost certain that there are no marfoo’ reports concerning this matter that can be relied upon, because the scholars who wrote comprehensively about the sciences of the Qur’aan and the dhikrs to be recited in connection with the Qur’aan, such as al-Nawawi, Ibn Katheer, al-Qurtubi and al-Suyooti, did not narrate anything other than what we have referred to above. If they had known of any reports with stronger isnaads, they would have quoted them.

Secondly: 

There is a saheeh report that Anas ibn Maalik (may Allaah be pleased with him) said du’aa’ when he completed the Qur’aan, and he would gather his family and children for that, and that a number of the Taabi’een followed him in that, as mentioned in the report of Mujaahid ibn Jabr (may Allaah have mercy on them all). 

Thirdly: 

There is no suggestion in the texts of Imam Abu Haneefah and Imam al-Shaafa’i (may Allaah have mercy on them) that this is Islamically prescribed. 

What is narrated from Imam Maalik (may Allaah have mercy on him) is that this is not something that the people did, and that completing the Qur’aan in night prayers in Ramadaan is not Sunnah. 

Fourthly: 

The view that it is mustahabb to make du’aa’ after completing the Qur’aan is what is narrated from Imam Ahmad (may Allaah have mercy on him), as our Hanbali scholars narrated from him, and as was affirmed by some later scholars of the other three madhhabs. 

2 – Du’aa’ following completion of the Qur’aan in prayer 

This may be summed up as follows:  

Firstly: 

From what is quoted above, there is no one letter from the Prophet (peace and blessings of Allaah be upon him) or from one of his companions (may Allaah be pleased with them) to indicate that it is Islamically prescribed to recite this du’aa’ in prayer after completing the Qur’aan, before or after bowing, whether that is done by an imam or by one who is praying alone. 

Secondly: 

The closest we can find on this matter is what was quoted by the scholars of our madhhab from the report from Imam Ahmad (may Allaah have mercy on him), according to the report of Hanbal, al-Fadl and al-Harbi, the isnaad of which we cannot find, about saying the du’aa’ for completing the Qur’aan in Taraweeh prayer before bowing. 

According to another report narrated from him – the source of which is not known – he allowed it in the du’aa’ of Witr. 

See Marwiyaat Du’aa’ Khatm al-Qur’aan. 

See also the answer to question no. 12949 

And Allaah knows best.