Will We See Allah in Jannah?
Question

Is it proven that the believers will see their Lord in the Hereafter?
Praise be to Allah.Proof for seeing Allah in Jannah from the Quran
The blessings which Allah bestows upon His slaves cannot be counted. Allah has singled out the believers for additional blessings in this world, as He has blessed them with Islam, and chosen them to be guided by the Quran, and He will bless them in Paradise with the greatest special blessing that He can bestow upon them, which is the honour of seeing His holy Face in the Paradise of `Adan , as He says (interpretation of the meaning): 
“Some faces that Day shall be shining (and radiant). Looking at their Lord (Allah).” [Al-Qiyamah :22-23]
I.e., the faces of the believers will be beautiful and radiant, joyful because they are looking at the Face of their Lord. Al-Hasan (may Allah have mercy on him) said: “They will look at their Lord and their faces will become radiant with His Light.” 
Ibn `Abbas (may Allah be pleased with him) said: “[The phrase] ‘Some faces that Day shall be shining (and radiant)’ means, because of the blessing. ‘Looking at their Lord’ means, looking upon the Face of their Lord.”  This is the opinion of the scholars who interpreted the Quran among the scholars of the Sunnah and Hadith. 
Allah says (interpretation of the meaning):  
“They will have all that they desire and We have more.” [Qaaf 50:35]
What is meant by “more” here is looking upon the Face of Allah, may He be Glorified and Exalted, as that was interpreted by `Ali and Anas ibn Malik (may Allah be pleased with them). 
Allah says (interpretation of the meaning): 
“For those who have done good is the best reward and even more.” [Yunus 10:26]
The “best reward” is Paradise, and “even more” is looking upon the Face of Allah, as explained by the Messenger of Allah (peace and blessings of Allah be upon him), in the narration by Muslim in (266) from Suhayb (may Allah be pleased with him), according to whom the Prophet (peace and blessings of Allah be upon him) said: 
“When the people of Paradise enter Paradise, Allah will say, ‘Do you want anything more?’ They will say, ‘Have You not brightened our faces, admitted us to Paradise, and saved us from Hell?’ Then the veil will be lifted and they will not have seen anything dearer to them than looking upon their Lord, may He be Glorified and Exalted. This is what is meant by ‘even more.’” Then he (peace and blessings of Allah be upon him) recited the verse (interpretation of the meaning): 
“For those who have done good is the best reward and even more .” [Yunus 10:26]
So, once you know that the people of Paradise will not be given anything there that is dearer to them than looking upon the Face of their Lord, it will become clear to you just how great is the deprivation and loss that awaits the sinners whom Allah warns with the words (interpretation of the meaning): 
“Nay! Surely, they (evil doers) will be veiled from seeing their Lord that Day.” [Al-Mutafiffun 83:15]
We ask Allah to keep us safe and sound 
How beautiful are the words of Ash-Shafi`i, which were narrated from him by Ar-Rabi` ibn Sulayman – who was one of his students – who said: “I was with Muhammad ibn Idris [i.e., Ash-Shafi`i], who had received a letter from Upper Egypt in which it said, ‘What do you say about the verse,  
“Nay! Surely, they (evil doers) will be veiled from seeing their Lord that Day.” [Al-Mutafiffun 83:15]
Ash-Shafi`i said: “Because they will be veiled by the wrath (of Allah), this indicates that the allies of Allah will see Him because He is pleased with them.’” 
This is some of the evidence from the Quran which proves that the believers will see their Lord in Paradise . 
Proof for seeing Allah in Jannah from the Sunnah
With regard to the evidence in the Sunnah, there is a great deal of it. For example: 

Al-Bukhari (6088) and Muslim (267) narrated from Abu Hurayrah (may Allah be pleased with him) that some people said: “O Messenger of Allah, will we see our Lord on the Day of Resurrection?” The Messenger of Allah said, “Do you doubt that you see the moon on the night when it is full?” They said, “No, O Messenger of Allah.” He said, “Do you doubt that you see the sun when there is no cloud?” They said, “No, O Messenger of Allah.” He said, “You will see Him likewise.” 

According to a report narrated by Al-Bukhari:  “you will not have any doubts or disputes concerning seeing Him,” and seeing Him will not cause you any hardship or make you tired. And Allah knows best. Summarised from Sharh Muslim. 

Also in Al-Bukhari (6883) and Muslim (1002), it is narrated that Jarir ibn ‘Abdullah (may Allah be pleased with him) said: “We were sitting with the Prophet (peace and blessings of Allah be upon him), looking at the moon on the night of the fourteenth (of the month). He said, ‘You will see your Lord with your own eyes just as you are looking at this (moon), without any doubt that you are seeing Him.’” 

The comparison in this Hadith is between seeing and seeing, i.e., just as we see the sun in all clarity on a cloudless day, and no one prevents anyone else from seeing it despite the large numbers of people looking at it, and just as we see the moon completely on the night when it is full, and we see it so clearly, despite the large numbers of people who are looking at it, so too the believers will see their Lord on the Day of Resurrection, so fully and clearly. But there is no comparison in the Hadiths between what is seen in one case and the other, may Allah be exalted far above such a thing, for there is nothing like unto Allah, and He is the All-Hearing, All-Seeing. 

Al-Bukhari (4500) and Muslim (6890) narrated from Abu Musa (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) said: “Two gardens of silver, their vessels and everything in them, and two gardens of gold, their vessels and everything in them. And there will be nothing preventing the people from seeing their Lord, may He be blessed and exalted, except the veil of pride concealing His Face in the Paradise of `Adan.” 

The Hadiths about seeing Allah were narrated by nearly thirty Companions. So whoever claims after this that no one will see Allah in the Hereafter is rejecting the Quran and the message with which Allah sent His Messengers, and he is exposing himself to the stern warning mentioned in the verse (interpretation of the meaning): 
“Nay! Surely, they (evil doers) will be veiled from seeing their Lord that Day.” [Al-Mutafiffun 83:15]
We ask Allah to keep us safe and sound, and we ask Him to bestow upon us the joy of seeing His holy Face…. Amen. 
References: 

Sharh al-‘Aqidah al-Tahawiyyah, 1/209 ff; 
A`lam As-Sunnah Al-Manshurah by Al-Hukami, p. 141.

For more details, please see the following answers: 164119 , 12423 , and 2734 . 
And Allah knows best.