Short answer
It comes from a sahih hadith in Muslim: the just will be on pulpits of light at the right of the Most Merciful, "and both His hands are right". Scholars explain that it removes any idea of deficiency, since in a human the left hand is the weaker one, and that "right" here is not a bodily limb. Allah's hand is an attribute mentioned in revelation, not a body part, and nothing is like Him.
Imam Abu Hanifa wrote in al-Fiqh al-Akbar that Allah has a hand, a face and a self as the Quran mentions, as attributes without asking how (bila kayf), and that it should not be said His hand is merely His power. Many later Maturidi and Ash'ari scholars also allowed a careful figurative explanation to keep people from imagining a body.
The four schools agree on this.
Explanation
The Prophet ﷺ said: "The just will be with Allah on pulpits of light at the right of the Most Merciful, and both His hands are right: those who are just in their rulings, with their families, and in what they are put in charge of." The hadith is in Sahih Muslim. In another sahih hadith he said Allah's hand is full, and spending day and night does not lessen it.
Why "both right"? In Arabic the right side stands for blessing, strength and honour, while a human's left hand is usually the weaker. Saying both are right removes any idea of weakness or lack from Allah. The Quran speaks of what Allah "created with My hands" (38:75), and it also says "There is nothing like unto Him" (42:11). Sunni creed holds both together.
The scholars took two careful approaches. The early way, followed by Imam Abu Hanifa, is tafwid: affirm the word as Allah said it, deny any likeness to creation, and leave its how to Allah. Many later scholars added ta'wil: explaining the word by a meaning that fits Allah, such as power, generosity or care, when people were at risk of picturing limbs. Both approaches aim to protect tawheed, and neither treats Allah as a body.
What is not allowed is to picture Allah with hands like ours, or to deny what the texts state. For related questions see what does Allah look like? and where is Allah?
The evidence
Quran, Surah Saad 38:75
قَالَ يَٰٓإِبْلِيسُ مَا مَنَعَكَ أَن تَسْجُدَ لِمَا خَلَقْتُ بِيَدَىَّ ۖ أَسْتَكْبَرْتَ أَمْ كُنتَ مِنَ ٱلْعَالِينَ ﴿٧٥﴾
[Allah] said, "O Iblees, what prevented you from prostrating to that which I created with My hands? Were you arrogant [then], or were you [already] among the haughty?"
Mentions Allah's hands in the Quran.
Quran, Surah Ash-Shura 42:11
فَاطِرُ ٱلسَّمَٰوَٰتِ وَٱلْأَرْضِ ۚ جَعَلَ لَكُم مِّنْ أَنفُسِكُمْ أَزْوَٰجًۭا وَمِنَ ٱلْأَنْعَٰمِ أَزْوَٰجًۭا ۖ يَذْرَؤُكُمْ فِيهِ ۚ لَيْسَ كَمِثْلِهِۦ شَىْءٌۭ ۖ وَهُوَ ٱلسَّمِيعُ ٱلْبَصِيرُ ﴿١١﴾
[He is] Creator of the heavens and the earth. He has made for you from yourselves, mates, and among the cattle, mates; He multiplies you thereby. There is nothing like unto Him, and He is the Hearing, the Seeing.
Rules out any likeness between Allah and creation.
Sahih Muslim 1827
Sahih... عَلَى مَنَابِرَ مِنْ نُورٍ عَنْ يَمِينِ الرَّحْمَنِ عَزَّ وَجَلَّ وَكِلْتَا يَدَيْهِ يَمِينٌ ...
"The just will be with Allah on pulpits of light at the right of the Most Merciful, and both His hands are right."
The source of the phrase.
Sahih al-Bukhari 7411
Sahih... يَدُ اللَّهِ مَلأَى لاَ يَغِيضُهَا نَفَقَةٌ ...
"Allah's hand is full; spending does not lessen it."
Another sahih text mentioning Allah's hand, in the sense of endless giving.
Where the ruling is recorded
- al-Fiqh al-Akbar (Imam Abu Hanifa), Section on the attributes of Allah. Affirms the hand, face and self of Allah as attributes without modality, and rejects saying His hand is only His power.
- Sharh al-Nawawi ala Sahih Muslim, Book of leadership, the hadith on the just rulers. Explains the hadith as one of the texts on the attributes, noting that "both His hands are right" rules out understanding the hand as a bodily limb.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.