What Are the Virtues of Duha Prayer?
Question

What are the Sahih Hadiths that have been narrated concerning the virtue of Duha prayer?
Praise be to Allah.Is Duha Prayer Sunnah or Obligatory?
Duha prayer is a confirmed Sunnah. It is soundly narrated from the Prophet (blessings and peace of Allah be upon him) that he did it, as it was narrated by Muslim (1176) from `Aishah (may Allah be pleased with her) that she said: The Messenger of Allah (blessings and peace of Allah be upon him) used to pray Duha with four Rak`ahs, and he would add whatever Allah willed.
He (blessings and peace of Allah be upon him) also used to tell his companions to do it, as we shall see below in the Hadiths.
Shaykh Ibn Baz (may Allah have mercy on him) said in Majmu‘ Al-Fatawa (11/389): Duha prayer is a confirmed sunnah which the Prophet (blessings and peace of Allah be upon him) did and told his companions to do it. End quote.
We have previously explained on our website that Duha prayer is prescribed, and the best time to offer this prayer, in the answers to questions no. 129956 and 22389 .
Key Hadiths Highlighting the Virtues of Duha Prayer
There are several Hadiths from the Prophet (blessings and of Allah be upon him) which speak of the virtues of Duha prayer, including the following:

It was narrated from Abu Dharr (may Allah be pleased with him), from the Prophet (blessings and peace of Allah be upon him) that he said: “In the morning a charity is due from every joint of one of you. Every Tasbihah is a charity, every Tahmidah is a charity, every Tahlilah is a charity, every Takbirah is a charity, enjoining what is good is a charity, forbidding what is evil is a charity, and two Rak`ahs offered in the forenoon (Duha) will suffice for that .” (Narrated by Muslim, 1181)

An-Nawawi (may Allah have mercy on him) said: The words of the Prophet (blessings and peace of Allah be upon him) “and two Rak`ahs offered in the forenoon (Duha) will suffice for that” are indicative of the great virtue of Duha and how important it is, and that it may be offered with two Rak`ahs.” (End quote from Sharh Muslim)

Al-Bukhari (1178) and Muslim (721) narrated that Abu Hurayrah (may Allah be pleased with him) said: My close friend (blessings and peace of Allah be upon him) advised me to do three things which I will never give up until I die: to fast three days of every month, to pray Duha, and to pray Witr before going to sleep.

It was narrated that Abu Ad-Darda’ (may Allah be pleased with him) said: My beloved (blessings and peace of Allah be upon him) advised me to do three things, which I will not give up so long as I live: to fast three days of each month, to pray Duha, and not to sleep until I pray Witr. (Narrated by Muslim, 1183)
Al-Qurtubi (may Allah have mercy on him) said: The Prophet’s advice to Abu Ad-Darda’ and Abu Hurayrah (may Allah be pleased with them) is indicative of the virtue of Duha, and that it will definitely be greatly rewarded. Hence they persisted in doing it and never omitted it.” (End quote from Al-Mufhim lima ashkala min Talkhis Muslim)

It was narrated from Abu Ad-Darda’ and Abu Dharr (may Allah be pleased with them) from the Messenger of Allah (blessings and peace of Allah be upon him), from Allah, may He be glorified and exalted, that He said: “O son of Adam, pray four Rak`ahs to Me at the beginning of the day, and I shall suffice you at the end of the day.” (Narrated by At-Tirmidhi, 437; classed as authentic by Shaykh Al-Albani)

Al-Mubarakfuri (may Allah have mercy on him) said: “at the beginning of the day”– it was said that what is meant is Duha prayer, or Salat Al-Ishraq [when the sun has risen to the height of a spear], or the Sunnah and obligatory prayer of Fajr, because it is the first obligatory prayer of the day. I say: the author and also Abu Dawud interpreted these Rak`ahs as referring to Duha prayer. Hence they included this Hadith in the Chapter on Duha Prayer. “I shall suffice you” with regard to your concerns “at the end of the day.”
At-Tibi said: That is, I shall suffice you with regard to your needs, and I shall ward off from you what you dislike, after your prayer and until the end of the day. What is meant is: focus on worshipping Me at the beginning of the day and I will grant you peace of mind at the end of the day, by helping you to meet your needs.” (End quote from Tuhfat Al-Ahwadhi  2/478)

It was narrated that Abu Hurayrah (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “No one persists in offering Duha prayer except one who often turns to Allah, for it is the prayer of those who often turn to Allah (Salat Al-Awwabin).” (Narrated by Ibn Khuzaymah; classed as sound by Al-Albani in Sahih At-Targhib wat-Tarhib, 1/164)
It was narrated from Anas ibn Malik (may Allah be pleased with him), from the Prophet (blessings and peace of Allah be upon him) that he said: “Whoever prays Fajr in congregation, then sits and remembers Allah until the sun rises, then prays two Rak`ahs, he will have a reward like that of Hajj and ‘umrah, complete, complete, complete.” (Narrated by At-Tirmidhi, 586; classed as sound by Shaykh Al-Albani (may Allah have mercy on him) in Sahih Sunan At-Tirmidhi)

Al-Mubarakfuri (may Allah have mercy on him) said in Tuhfat Al-Ahwadhi bi Sharh Jami` At-Tirmidhi (3/158): the words: “then prays two Rak`ahs” mean: after the sun has risen. At-Tibi said: That is, then he prays after the sun has risen to the height of a spear, when the time when it is disliked to pray has ended. This prayer is called Salat Al-Ishraq and it marks the beginning of the time for Duha prayer. (End quote)
For more details, please see the following answers:
Should One Make Up Duha Prayer?
Can You Pray Duha If You Missed Fajr?
Can You Pray Duha at Work?
And Allah knows best.