It said Michael Adebolajo, 28, was arrested there and it gave consular assistance “as normal” in the circumstances.
Michael Adebolajo was believed to have been preparing to fight with Somali militant group al-Shabab, a Kenyan government spokesman confirmed, and was later deported.
Meanwhile, police investigating soldier Lee Rigby’s murder have arrested a 22-year-old man in north London.
The arrest at Highbury Grove, on suspicion of conspiracy to murder, brings the total number made so far in the case to nine.
Members of Lee Rigby’s family have visited the scene of the killing, laying flowers at Woolwich Barracks where the 25-year-old drummer with the Royal Regiment of Fusiliers was based.
They hugged and comforted each other as they looked at some of the many thousands of floral tributes that have been left in his memory, before crossing the road to look at the exact spot where he was attacked.
Several hundred people gathered at the scene a few hours later, some chanting Lee Rigby’s name and waving Help for Heroes flags.
The Met Police said it was a planned community event in which a group of people intended to lay a wreath.
A small group of English Defence League members also joined the crowd, prompting organizers to complain that their plans had been “hijacked”.
The Kenyan government had previously denied that Michael Adebolajo had ever visited the country, but spokesman Muthui Kariuki said there had been some confusion as he was arrested under a different name.
In video footage of his court appearance which emerged on Sunday, Michael Adebolajo is heard to say: “These people are mistreating us, we are innocent.”
Muthui Kariuki said Michael Adebolajo was then handed over to “British security officers” when it emerged he was a UK citizen.
Islamist insurgent group al-Shabab is affiliated to al-Qaeda and is thought to have 7,000 to 9,000 fighters. It killed 76 people in a double bomb attack in Uganda as they watched the 2010 World Cup.
Michale Adebolajo and a second man, Michael Adebowale, 22, were arrested on suspicion of the murder of soldier Lee Rigby in Woolwich on Wednesday.
They remain in custody in hospital in a stable condition after being shot and wounded by police at the scene after the killing.
Three further men, aged 21, 24 and 28, were arrested in London on Saturday evening on suspicion of conspiracy to commit murder – a Taser was used on two of them.
A 29-year-old man arrested earlier on suspicion of conspiracy to murder was released on bail on Saturday, while two women aged 29 and 31, arrested on Thursday, have been released without charge.
In an update on Sunday, Metropolitan Police Deputy Assistant Commissioner Stuart Osborne said officers were examining CCTV footage, social media and forensic material as part of their investigation into Drummer Lee Rigby’s murder.
He appealed for any associates of Michael Adebolajo and Michael Adebowale who believed they might have useful information to come forward.
Earlier on Sunday, Home Secretary Theresa May said “500 officers and others” were working on the case, including counter-terrorism officers brought in from elsewhere in the country.
Senior Whitehall sources have previously confirmed both suspects arrested at the scene of Drummer Lee Rigby’s killing were already known to security services.
When asked if there were mistakes made by the security services in dealing with this case, Theresa May said: “What we have is the right procedures which say when things like this happen we do need to look at whether there are any lessons to be learned.”
Theresa May also said a new taskforce was being set up to look at whether new powers were needed to tackle extremism.
It will be chaired by the prime minister and include senior cabinet ministers and security chiefs.
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