Michael Adebolajo, 28, described the killing as a “military operation”.
He also told the Old Bailey he loved extremist network al-Qaeda.
The prosecution says he and Michael Adebowale, 22 – who also denies murder – rammed Fusilier Rigby with a car in Woolwich, south-east London, on 22 May, before attacking him with knives.
They are also both accused of attempting to murder a police officer and conspiracy to murder a police officer.
Under cross examination by prosecutor Richard Whittam QC, Mr Adebolajo replied “yes” when he was asked if he had killed Fusilier Rigby, describing it as a “military operation”.
Fusilier Rigby's widow Rebecca left the courtroom in tears as Mr Adebolajo claimed the soldier was still moving after being hit by the car.
He refused to answer questions about how long he had planned the attack, but said he had not planned to run down Fusilier Rigby, saying “it just so happened that Allah caused him to cross in front of my car.”
He described attacking Fusilier Rigby with a meat cleaver in graphic detail, and said the soldier was already dead by the time Mr Adebowale had joined him in attacking the soldier.
Earlier the court heard Mr Adebolajo, from Romford, east London, give his name as Mujaahid Abu Hamza and confirm he was married with six children, including a seven-year-old boy and a baby who was four days old on the day of the incident.
He said he had been brought up as a Christian by his family and his parents had taken him to church every Sunday.
“The memory that sticks in my mind… is probably every New Year's Eve in the evening around 11 o'clock we would gather around in candlelight and read passages from the Bible,” he said.
He converted to Islam in his first year as a student at Greenwich University.
He told the court: “My religion is everything.
“When I came to Islam I realised that… real success is not just what you can acquire, but really is if you make it to paradise, because then you can relax,” he added.
Of al-Qaeda, Mr Adebolajo said: “Al-Qaeda I consider to be Mujahideen. I love them, they're my brothers. I have never met them. I consider them my brothers in Islam.”
Last week the jury heard detailed and, at times, graphic detail of the prosecution's version of the events of 22 May, when 25-year-old Fusilier Rigby, of Middleton, Greater Manchester, was killed as he returned to Woolwich Barracks.
In one of the interviews Mr Adebolajo said soldiers were the “most fair target” because they joined the Army “with kind of an understanding that your life is at risk”.
In court on Monday he said he had prayed the night before that he would target the right person.
“To be 100%, I don't believe there's a way to know 100% that was a soldier, however there were some steps that we took. For example before we started out on that day and the night previous to that I started worshipping Allah and begging him that… we strike a soldier and a soldier only.”
He said he knew Fusilier Rigby was a soldier because of the camouflage backpack he was carrying and because he was going towards the barracks.
'Brainwashed by BBC'
When he was later asked what his defence to the charge of murder was, he said: “I am a soldier. I'm a soldier of Allah”.
He continued: “I understand that some people might not recognise this because we do not wear fatigues and we do not go to the Brecon Beacons and train and this sort of thing. But we are still soldiers in the sight of Allah as a mujahid.
“This is all that matters, if Allah considers me a soldier, then I am a soldier.”
Last week, the court was shown mobile phone footage of Mr Adebolajo in the aftermath of the attack.
On Monday he said he wanted to film the scene of the attack to get his message across without people being brainwashed by the BBC.
He said he was “almost certain” he would be shot and killed by the firearms officers who arrived at the scene of the attack in Woolwich.
Last week, CCTV footage of him running towards the police car with a meat cleaver raised was shown to the court.
He complained on Monday that the officers had not shot him in the head but said he had no grievance with them, because they were “just doing their duty”.
He said he should be ransomed back to other jihadi fighters, set free or killed if he was found guilty.
Earlier, he told the court the “vast majority” of his friends growing up in Romford had been white and British.
One of them, Kirk Redpath, joined the Army and was later killed in Iraq.
Mr Adebolajo said: “I hold Tony Blair responsible for his death.”
The defendant told the court that he had tried to travel to Somalia in 2010 but was captured in Kenya and returned to the UK.
The trial continues on 10th December.