He wants to marry a girl with whom he had a relationship

Firstly: 

Before answering your question, we must remind you that it is obligatory to repent and regret what you have done with this woman, because you have fallen into several major sins, the most serious of which is zina (fornication) which is clearly forbidden in the Qur’aan and Sunnah, and the scholars are unanimously agreed that it is haraam, and wise people are unanimously agreed that it is abhorrent and evil. 

Allaah says (interpretation of the meaning): 

“And come not near to unlawful sex. Verily, it is a Faahishah (i.e. anything that transgresses its limits: a great sin), and an evil way that leads one to hell unless Allaah forgives him)”

[al-Isra’ 17:32]

And the Prophet (peace and blessings of Allaah be upon him) said: “No adulterer is a believer at the time when he is committing adultery.” Narrated by al-Bukhaari (2475) and Muslim (57).  

There is a severe punishment for zina in al-Barzakh, before the punishment in the Hereafter. In the famous hadeeth of Samurah ibn Jundub (may Allaah be pleased with him) about the dream, it says:  

“… then we [i.e., the Prophet (peace and blessings of Allaah be upon him) and Jibreel and Mikaa’eel] proceeded and came to something like a tannoor (a kind of oven), in which there were clamouring voices.” He [the Prophet (peace and blessings of Allaah be upon him)] said: “We looked into it and there we saw naked men and women. Flames were coming to them from the bottom of it, and when the flames reached them, they made uproar. I said to them [i.e., the two angels who were accompanying him], ‘Who are these?’ … They said, ‘We will tell you. As for the naked men and women in the structure that resembled a tannoor oven, they are the adulterers and adulteresses.’” 

Narrated by al-Bukhaari (6640). 

Allaah has ordained the hadd punishment for zina. He says concerning the hadd punishment for an unmarried person (interpretation of the meaning): 

“The fornicatress and the fornicator, flog each of them with a hundred stripes. Let not pity withhold you in their case, in a punishment prescribed by Allaah, if you believe in Allaah and the Last Day. And let a party of the believers witness their punishment”

[al-Noor 24:2]

As for the person who has previously been married, the hadd punishment is execution, In the hadeeth narrated by Imam Muslim in his Saheeh (3199) it is narrated that the Prophet (peace and blessings of Allaah be upon him) said: “For a previously-married person with a previously-married person, [the punishment is] one hundred lashes and stoning.” 

What we have said to you applies to the woman too, and she should realize that her sin is even worse, but because, as you say, she has become righteous, we hope that her repentance is sincere and that Allaah will forgive her by His grace and kindness. 

Secondly: 

You should note that if you have not both repented from the sin of zina, then it is not permissible for you to marry her, because Allaah has forbidden the zaani and zaaniyah to marry unless they both repent. Allaah says (interpretation of the meaning): 

“The adulterer — fornicator marries not but an adulteress — fornicatress or a Mushrikah; and the adulteress –fornicatress, none marries her except an adulterer — fornicater or a Mushrik [and that means that the man who agrees to marry (have a sexual relation with) a Mushrikah (female polytheist, pagan or idolatress) or a prostitute, then surely, he is either an adulterer — fornicator, or a Mushrik (polytheist, pagan or idolater). And the woman who agrees to marry (have a sexual relation with) a Mushrik (polytheist, pagan or idolater) or an adulterer — fornicator, then she is either a prostitute or a Mushrikah (female polytheist, pagan, or idolatress)]. Such a thing is forbidden to the believers (of Islamic Monotheism)”

[al-Noor 24:3]

Shaykh ‘Abd al-Rahmaan al-Sa’di (may Allaah have mercy on him) said: 

This clearly points to the abhorrent nature of zina, and that is tarnishes the honour of the one who does it in a way that other sins do not. Allaah tells us that no woman would marry a zaani but a woman who is also a zaaniyah, who is like him, or a mushrik woman who associates others with Allaah and does not believe in the Resurrection or in reward and punishment (in the Hereafter), and who does not adhere to the commands of Allaah. And similarly, no one would marry a zaaniyah except a zaani or a mushrik. “Such a thing is forbidden to the believers” means, it is haraam for them to marry zaanis or zaaniyahs. 

What the verse means is that if a person wants to marry the man or woman who commits zina and has not repented from that, despite the fact that Allaah has prohibited that, then he is either not adhering to the ruling of Allaah and His Messenger, in which case he cannot be anything but a mushrik, or he is adhering to the ruling of Allaah and His Messenger but he agrees to this marriage despite knowing that this person has committed zina, in which case this marriage is also zina, and he is an immoral zaani. If he truly believed in Allaah, he would not do that. This clearly indicates that it is haraam to marry a zaaniyah unless she repents, or to marry a zaani unless he repents, because marriage is the strongest type of companionship, and Allaah says (interpretation of the meaning): “Assemble those who did wrong, together with their companions” [al-Saaffaat 37:22]. Allaah has forbidden that because of what it involves of great evil, and lack of protective jealousy, and attribution of children who are not his to the husband, and the zaani failing to keep her chaste because he is distracted elsewhere, any one of which is sufficient reason for the prohibition. End quote. 

Tafseer al-Sa’di (p. 561). 

The scholars of the Standing Committee were asked: 

A man committed zina with a virgin and wants to marry her. Is it permissible for him to do that? 

They replied: 

If the matter is as described, each of them must repent to Allaah and give up this sin, and regret what has happened of immoral actions, and resolve not to do it again, and do a lot of good deeds, in the hope that Allaah will accept their repentance and turn their bad deeds into good. Allaah says (interpretation of the meaning): 

“And those who invoke not any other ilaah (god) along with Allaah, nor kill such person as Allaah has forbidden, except for just cause, nor commit illegal sexual intercourse ___ and whoever does this shall receive the punishment.

69. The torment will be doubled to him on the Day of Resurrection, and he will abide therein in disgrace;

70. Except those who repent and believe (in Islamic Monotheism), and do righteous deeds; for those, Allaah will change their sins into good deeds, and Allaah is Oft‑Forgiving, Most Merciful

71. And whosoever repents and does righteous good deeds; then verily, he repents towards Allaah with true repentance”

[al-Furqaan 25:68-70]

If he wants to marry her, then he must wait for one menstrual cycle to establish whether her womb is empty before doing the marriage contract with her. If it turns out that she is pregnant, then it is not permissible for him to do the marriage contract with her until after she gives birth, in accordance with the hadeeth in which the Prophet (peace and blessings of Allaah be upon him) forbade a man to water the crop of another with his own water. End quote. 

Fataawa Islamiyyah (3/247). 

So repent to Allaah and set your affairs straight, and do a lot of good deeds, and after that it will be permissible for you to get married. We ask Allaah to accept your repentance and to forgive you, by His grace and mercy. 

See also question no. 85335. 

And Allaah knows best.