Michael Adebolajo was believed to have been preparing to train and fight with the al-Qaeda-linked Somali militant group al-Shabab in 2010 when he was arrested with five others, Kenya's anti-terrorism police unit head Boniface Mwaniki said.
The revelations came as London's Metropolitan Police said specialist firearms officers arrested another man suspected of conspiring to murder 25-year-old soldier Lee Rigby. Police did not provide details about the suspect, only saying he is 22 years old.
The latest arrest followed the detainment in London late Saturday of three others, aged 21 to 28, also suspected in the case.
Adebolajo, 28, and Michael Adebowale, 22, are the main suspects in the killing and remained under armed guard in separate London hospitals.
Mwaniki said Adebolajo was deported after his arrest in 2010. "Kenya's government arrested Michael Olemindis Ndemolajo. We handed him to British security agents in Kenya and he seems to have found his way to London and mutated to Michael Adebolajo," Kenya government spokesman Muthui Kariuki said.
When asked about reports that British embassy officials were involved, a Foreign Office statement said: "We can confirm a British national was arrested in Kenya in 2010. The Foreign and Commonwealth Office provided consular assistance as normal for British nationals."
UK sets up team to tackle radical preachers, groups
Britain's government is setting up a new terrorism task force to tackle radical preachers and extremism, officials said Sunday, days after suspects apparently linked to extremist Islamist activists brutally killed a British soldier in London.
Home Secretary Theresa May said the group will look at whether new powers and laws are needed to clamp down on religious leaders and organisations who target potential recruits in jails, schools and mosques.
Thousands of people are at risk of being radicalised in Britain, May told the BBC. The force will include senior ministers, London's police chief and the head of the MI5 security service.