Medouni, 40, said when he first met Kouider in 2001 she was "very, very beautiful" and when he kissed her he felt as if he had won the Euromillions lottery.
He said they had an on and off relationship for the next 17 years, even though she repeatedly cheated on him.
Medouni and Kouider, 35, both deny murdering 21-year-old Sophie and each claims the other was responsible for her death.
They have both admitted perverting the course of justice by disposing of the body.
The pair were arrested by police who found Medouni burning the body in the back garden of their home in Southfields, south-west London.
Claimed He Was Burning a Sheep
When questioned he told them he was burning a sheep's carcass.
The court has heard audio recordings the couple made when they interrogated Sophie over allegations she had colluded with Kouider's ex-boyfriend Mark Walton, a founder member of the popular boy band Boyzone.
Medouni's barrister, Orlando Pownall QC, asked his client a series of questions at the start of his evidence to the Old Bailey on Monday, April 16.
"Did you cause the death of Sophie Lionnet by your own hand?" asked Mr. Pownall.
"No," replied Medouni, a balding and softly-spoken figure, who wore a blue suit, white shirt and gray tie.
"Was Sophie Lionnet's death caused by a plan or agreement between you and Sabrina Kouider?" asked Mr. Pownall.
"No," he replied.
"Did you burn her body?" asked Mr. Pownall.
"Yes," replied Medouni.
"Do you accept that you made many dreadful decisions in the account you are about to give?" asked Mr. Pownall.
"Yes," he replied.
Made Redundant in 2012
Medouni, who was made redundant by the Societe Generale bank in 2012, gave evidence about his relationship with Kouider, who he met in Paris in 2001 when she was 19.
He said she slept with another man only weeks after they got together, when he was working away in Luxembourg.
"That was my first time of falling in love (and when she told me) I felt like the world fell apart. I was very unhappy," Medouni told the court.
According to his version of events it was a pattern which repeated itself over the years.
He said they went on holiday together to Greece in June 2007 but as soon as they got back to London she returned to Paris.
When she returned two months later she was pregnant by another man.
But he stayed with her because he loved her and when he used the present tense, Mr. Pownall asked him if he still loved her now.
"Yes, I still love her," he replied.
Co-Defendant Shook Her Head
Medouni, who sat listening intently in the dock, shook her head repeatedly and muttered to herself as he gave his testimony.
He said Kouider would often "go mad" at him for no reason and on one occasion brandished a knife and threatened to harm herself.
He said she would dream about him being with another woman and would imagine it was real.
[Tweet: "What Ouissem Medouni said in his defense"]
Medouni said she was the "dominant" partner in their relationship and her moods would go "up and down very quickly in the space of seconds."
"In the last year, every morning she would wake up screaming for nothing. If she had a dream about me being with another woman, she said it was going to happen and make up a story in her mind about it," he said.
"She said she had a gift for knowing what is going to happen," added Medouni, who said she would sometimes refer to him as "her cousin" in public, even though they were not related.
Medouni also gave evidence about the violence which he claimed Kouider meted out to Sophie, when she came to live with them in January 2016.
Victim's Family in Court
Sophie's mother Catherine and grandfather Stephane Devalonne, who had travelled from her home town of Troyes, were in court as he described her as a "shy" girl who would stay in her room and read a lot.
He said he had once, in July 2017, stepped in to stop Kouider beating Sophie.
"I messed up. I should have done. I should have sent her home. I hate myself because there was this occasion and when I think about that conversation I'm really, really angry at myself," Medouni told the court.
Two months later, on September 18, Sophie was dead and the couple were both later arrested.
The trial continues.