Specialist officers from the NCA’s National Extradition Unit apprehended Robert James Purkiss in Tidworth on Thursday, November 6.
A warrant for his arrest was issued in September.
The 38-year-old appeared at Westminster Magistrates’ Court on Friday, November 7, so that extradition proceedings could begin.
He was remanded into custody until his next appearance which will be at the same court on Friday, November 14.
The suspect, of Greater Manchester, previously served as a medic with the Duke of Lancaster regiment – including on tours of Afghanistan.
The Sunday Times previously reported that Purkiss is accused of a single count of murdering Agnes Wanjiru on the night of March 31, 2012.
An inquest in 2018 concluded Ms Wanjiru was murdered by British soldiers after she was discovered near a British Army base, two months after she disappeared.
Police in Kenya reopened the case into Ms Wanjiru’s murder in 2021 after her family said they were upset no-one had been convicted of the killing.
A post-mortem examination concluded she died as a result of stab wounds to her chest and abdomen.
