Gilbert Deya, the self-proclaimed bishop of Gilbert Deya Ministries, is charged with five counts of child stealing between 1999 and 2004.
Mr Deya’s wife, Mary Deya, has already been convicted of child stealing offences in Nairobi.
Lawyers for London-based Mr Deya said he had been unfairly targeted and will appeal against the extradition order.
The orders can be automatically appealed, meaning the Kenyan government’s attempt to have Mr Deya returned to face trial could continue in British courts for months.
The home secretary will make the final decision on whether he should be extradited.
At the extradition hearing, District Judge Caroline Tubbs heard from the lawyer for the Kenyan government that they had sufficient evidence to prosecute Mr Deya for child stealing after a group of small children were discovered in his Nairobi home.
The discovery came after media reports in both Kenya and Britain in August 2004 about the arrival of ‘miracle babies’ to members of Mr Deya’s UK-based evangelical church.
Police in both countries subsequently investigated and Kenyan authorities used DNA testing to discover that none of the small children in the Deya home in Nairobi were the biological children of either Mr or Mrs Deya – contrary to what the couple said.
In an interview with British police in November 2004, Mr Deya said he was the father of the children in question.
All five children were taken into care in Kenya and none of their birth parents have been traced.
In Britain, one couple who say Mr Deya produced a ‘miracle baby’ in Kenya for them had the child taken away from them by Haringey Borough Council after it emerged that they were not the child’s parents.
The child, who has since been adopted, was brought into Britain using fake birth registry documents.
Mr Deya’s lawyers have argued that he is the victim of a political vendetta by senior politicians in Kenya and so should not be extradited.
Lawyer Ben Cooper argued that Mr Deya’s high-profile opposition to the government means that he will not be assured of a fair trial.
Mr Cooper further argued that prison conditions in Kenya do not meet the requisite standard for extradition.
Adina Ezekiel, representing the government of Kenya, told the court that there was no evidence to suggest any political motives behind the extradition request.
Mr Deya was described as “cool” as the decision was announced. After the decision, his brother Amos said they had been expecting this ruling and they planned to appeal.