Virtues of Tawaf Around the Sacred House
Question

What are the sahih hadiths about the virtues of voluntary tawaf?
Praise be to Allah.Significance of tawaf
Tawaf or circumambulation of the Ka‘bah is a great act of worship, and is one of the visible symbols of Islam. It has been prescribed since the Ka‘bah was built. Allah, may He be exalted, says (interpretation of the meaning):
“and We commanded Ibrahim (Abraham) and Ismail (Ishmael) that they should purify My House (the Ka‘bah at Makkah) for those who are circumambulating it, or staying (I’tikaf), or bowing or prostrating themselves (there, in prayer).” [al-Baqarah 2:125]
“And (remember) when We showed Ibrahim (Abraham) the site of the (Sacred) House (the Ka‘bah at Makkah) (saying): "Associate not anything (in worship) with Me, (La ilaha ill-Allah (none has the right to be worshipped but Allah Islamic Monotheism), and sanctify My House for those who circumambulate it, and those who stand up for prayer, and those who bow (submit themselves with humility and obedience to Allah), and make prostration (in prayer, etc.).” [al-Hajj 22:26] 
Virtues of tawaf 
There are a number of hadiths and reports which speak of the virtues of circumambulating the House (tawaf) , of which we will mention the following: 
Imam Ahmad (4462), at-Tirmidhi (959) and an-Nasai (866) narrated that Ibn ‘Umar (may Allah be pleased with him) said with regard to touching the Black Stone and Yemeni Corner in tawaf: I heard the Messenger of Allah (blessings and peace of Allah be upon him) say: “Touching them erases sins.” 
He said: And I heard him say: “Whoever circumambulates (the Ka‘bah) seven times , counting them, and then prays two rak‘ahs (after tawaf) it will be equivalent to his freeing a believing slave.” 
He said: And I heard him say: “No man lifts his foot and sets it down but ten hasanat (good deeds) will be recorded for him, and ten sayyiat (bad deeds) will be erased from his record, and he will be raised thereby ten degrees in status.” (Classed as hasan by Ahmad Shakir and al-Arnaut in Tahqiq al-Musnad)
The version narrated by at-Tirmidhi says: “He does not set down one foot and lift the other but Allah will erase one sin from his record and will record for him one hasanah (good deed) thereby.” (Classed as sahih by al-Albani in Sahih at-Tirmidhi)
As-Sindi said:
“It – namely tawaf – is equivalent to freeing a slave, in terms of reward.” 
Abu Dawud (1888) and at-Tirmidhi (902) narrated that ‘Aishah said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Circumambulation of the House , going between as-Safa and al-Marwah, and stoning of the Jamarat were only ordained in order to establish the remembrance of Allah.” (Classed as sahih by at-Tirmidhi and by Ibn Qudamah in al-Kafi (1/516). Ibn Baz said in his Fatawa (16/186): It is thabit (proven). It was classed as da‘if by al-Albani in Da‘if Abi Dawud.) 
An-Nasai (2922) and Ahmad (15423) narrated from Tawus, from a man who met the Prophet (blessings and peace of Allah be upon him), that the Prophet (blessings and peace of Allah be upon him) said: “Tawaf is prayer, so when you do tawaf, speak little.” 
At-Tirmidhi (960) narrated from Ibn 'Abbas, that the Prophet (blessings and peace of Allah be upon him) said: “Tawaf around the House is like prayer, except that you may speak during it. So whoever speaks during it, let him not speak of anything but what is good.” (Classed as sahih by al-Albani in Sahih at-Tirmidhi)
And Allah knows best.