Firstly: 

it was narrated from Ibn Maajah (4250), at-Tabaraani in al-Mu‘jam al-Kabeer (10281), Abu Nu‘aym in Hilyat al-Awliya’ (4/210), al-Bayhaqi in as-Sunan (20561), via Abu ‘Ubaydah ibn ‘Abdullah ibn Mas‘ood, that his father said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “The one who repents from sin is like one who did not sin.” 

Its men are thiqaat (trustworthy), except that Abu ‘Ubaydah did not hear from his father, so it is munqati‘ (interrupted). See: at-Tahdheeb (5/65) 

But it is proven because of corroborating evidence, therefore some of the scholars classed it as hasan and others classed it as saheeh. 

Al-Haafiz said in al-Fath (13/471): Its isnaad is hasan. 

Ibn Muflih said in al-Adaab ash-Shar‘iyyah (1/87): Its men are all thiqaat (trustworthy). 

As-Sakhkhaawi said in al-Maqaasid al-Hasanah (p. 249): Its men are thiqaat; indeed, our shaykh classed it as hasan because of its corroborating evidence. 

It was also classed as hasan by as-Suyooti in al-Jaami‘ as-Sagheer (3386), and by al-Albaani in Saheeh al-Jaami‘ (3008). It was classed as saheeh by Ibn Baaz in Majmoo‘ al-Fataawa (10/314) 

There is corroborating evidence in the hadeeth of ‘Aa’ishah which was narrated by al-Bayhaqi (6640); its isnaad is da‘eef. 

There is also corroborating evidence in the hadeeth of Ibn ‘Abbas that was narrated by al-Bayhaqi in ash-Shu‘ab (6780); its isnaad is waahin (flimsy). 

There is a fourth corroborating report in the hadeeth of Abu Sa‘d al-Ansaari that was narrated by Abu Nu‘aym in al-Hilyah (13/398) and at-Tabaraani in al-Kabeer (775), but its isnaad is da‘eef. 

Secondly: 

In some reports, the hadeeth was narrated with some additional material that is da‘eef (weak), such as the report which says: “The one who repents from sin is like one who did not sin, and if Allah loves a person, sin will not harm him.” This is a da‘eef (weak) addition. 

See: Silsilat al-Ahaadeeth ad-Da‘eefah wa’l-Mawdoo‘ah (615). 

The same may be said of the report which says: “The one who repents from sin is like one who did not sin, and the one who prays for forgiveness from sin whilst persisting in it is like one who mocks his Lord, and the one who annoys a Muslim will have a burden of sin like the number of palm trees.” This additional material is da‘eef.

See: Silsilat al-Ahaadeeth ad-Da‘eefah wa’l-Mawdoo‘ah (616). 

The same may be said of the report which says: “Death is a fortune, sin is a calamity, poverty is rest, wealth is a punishment, reason is a gift from Allah, ignorance is misguidance, wrongdoing is regret, obedience is a joy, weeping from fear of Allah is salvation from the Fire, laughter is destruction of the body, and the one who repents from sin is like one who did not sin.” This additional material is munkar (odd). 

See: Silsilat al-Ahaadeeth ad-Da‘eefah wa’l-Mawdoo‘ah (6526). 

With regard to the report, “Regret is repentance and the one who repents is like one who did not sin,” its narration is proven. 

See: Saheeh al-Jaami‘ as-Sagheer (6803) 

Thirdly: 

What the hadeeth means is: if a person commits a sin, then repents sincerely from it, gives it up, regrets having done it, prays for forgiveness and does not go back to it, Allah will accept his repentance and treat him like one who did not sin; in fact, He will turn his bad deeds into good deeds, and He will love him and make him one of His pious slaves, because he repented to his Lord, turned to Him because of his love for Allah, his keenness to please Him, and his fear of Him, and these are the characteristics of the pious. 

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: 

The one who repents from sin is like one who did not sin, and if the sin is removed, then the punishment and consequences are also removed. 

End quote from Sharh al-‘Umdah (4/39) 

He also said: 

The one who repents from sin is like the one who did not sin; as that is the case, he is included among those who fear Allah and thus deserves that Allah should grant him relief and a way out, for our Prophet Muhammad (blessings and peace of Allah be upon him) is the Prophet of mercy, so everyone who repents will have a way out according to his teachings, unlike the teachings of those who came before us, for among them the one who repented would still be punished with penalties such as killing themselves and so on.

End quote from Majmoo‘ al-Fataawa (33/35) 

Ibn al-Qayyim (may Allah have mercy on him) said: 

Moreover, Allah, may He be exalted, makes the one who repents from sin like the one who did not sin. So whoever meets Him having repented sincerely, He will not punish him for that from which he has repented. Similarly, in terms of rulings in this world, if a person repents sincerely before being brought to the ruler, the hadd punishment is waived in his case, according to the more correct of the two scholarly opinions. But if he has been brought to the ruler, then his repentance will not cause the hadd punishment to be waived from him, and that is lest this be taken as a means to evade the hadd punishments decreed by Allah.

End quote from I‘laam al-Muwaqqi‘een (3/115) 

He also said: 

Allah, may He be glorified, has guaranteed to the one who repents from shirk (associating others with Allah), murder and zina (fornication or adultery) that He will turn his bad deeds into good deeds. This is a general ruling which applies to everyone who repents from sin. 

Allah, may He be exalted, says (interpretation of the meaning):

“Say: O ‘Ibaadi (My slaves) who have transgressed against themselves (by committing evil deeds and sins)! Despair not of the Mercy of Allah, verily, Allah forgives all sins. Truly, He is Oft‑Forgiving, Most Merciful”

[al-Zumar 39:53]. 

Not a single sin is excluded from this general meaning, but this applies specifically to those who repent.

End quote from al-Jawaab al-Kaafi (p. 165) 

He also said: 

As the one who repents from sin is like the one who did not sin, and the effect of sin is erased by repentance, then it becomes as if it never happened.

End quote from Tareeq al-Hijratayn (p. 231) 

Al-Qaari (may Allah have mercy on him) said: 

It should be understood that if repentance meets all the required conditions, then it will undoubtedly be accepted and result in forgiveness, because Allah, may He be exalted, says (interpretation of the meaning): “And He it is Who accepts repentance from His slaves” [ash-Shoora 42:25]. And it is not possible for Him to break His promise.

End quote from Mirqaat al-Mafaateeh (4/1337) 

Thirdly: 

For information on what is meant by a hasan hadeeth, the definition and categories thereof, and the ways in which the scholars quote such reports as evidence, please see the answer to question no. 196606 

For more information, please see the answers to questions no. 47748 and 79163

And Allah knows best.