According to an anti-terrorism police official, Michael Adebolajo was arrested while apparently preparing to train and fight with al Qaeda-linked Somali militants.
Kenyan officials said Adebolajo, who was carrying a British passport, was then handed over to British authorities in the East African country.
Adebolajo was arrested with five others near Kenya's border with Somalia, Kenya's anti-terrorism police unit chief Boniface Mwaniki told The Associated Press. Police believed Adebolajo was going to work with Somali militant group al-Shabab.
According to Mwaniki, Adebolajo was deported from Kenya after his arrest. Kenya's government spokesman said he was arrested under a different name, and taken to court before being handed to British authorities.
This latest information surfaced as London's Metropolitan Police said specialist firearms officers arrested a man on Sunday, who is suspected of conspiring to murder 25-year-old British soldier Lee Rigby. Police gave few details about the suspect, only saying he is 22 years old.
A total of nine suspects have been taken into custody regarding Rigby's horrific killing in London. Two have been released without charge, and one was released on bail pending further questioning. No one has been charged in the case.
The British soldier, who had served in Afghanistan, was run over, then stabbed with knives in the Woolwich area in southeast London on Wednesday afternoon as he was walking near his barracks.
Adebolajo, 28, and Michael Adebowale, 22, are the main suspects in the killing and remained under armed guard in separate London hospitals after police shot them at the scene.
Meantime, Rigby's grieving family visited the scene of his killing in London on Sunday, pausing for a few moments in reflection and laying flowers to join the hundreds of floral tributes already left at the nearby Woolwich Barracks by well-wishers.
The Associated Press contributed to this report.