The scandal first broke in 2004 as it emerged Deya and his wife Mary claimed their prayers could see infertile and post-menopausal women fall pregnant in four months, and without intercourse.
However the "miracle babies" were allegedly stolen, mainly from Nairobi's Pumwani Maternity Hospital.
Kenya plans to charge Deya with five counts of abducting children aged between 12 months and four-and-a-half years.
The children were allegedly kidnapped between 1999 and 2004 in Kenya.
His wife is already serving a three-year jail term on similar charges.
Deya's extradition was first ordered in 2007, after he exhausted all avenues of appeal.
The controversial preacher landed back in Nairobi before dawn, and investigators "are preparing to take him to court", said inspector general of police Joseph Boinnet.
Deya has been running his Gilbert Deya Ministries operation from Peckham, south London. His church's website says it has a membership of more than 34,000 in Britain.
He claims he was consecrated as an archbishop in the United States in 1992.
According to local media Deya was an evangelist in Kenya in the late eighties and early nineties, before he moved to the UK to set up his ministry.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)