Allen was picked up from Vishakapatam, Andhra Pradesh, where he had gone absconding since November 5, the day Mary Ellen had lodged a complaint.
Police said that the medical examinations that have been conducted on Allen and some children revealed that the accused had abused the children for a period of over one year.
"The medical examinations were conducted. He is totally involved in this crime. After the examination, he was produced before the court. Now he is remanded to judicial custody," said Debi Prakash Dash, Officer In charge, Sadar Piolice Station, Puri.
Mary Ellen, who runs the Mary Ellen Berger Foundation, said that she carried out her own investigations and talked to the children and found out that their version was in line with that of the staff and another friend who had also hinted towards the same.
"I made my own investigations during...talking to the children. Because it was difficult at the very movement, the first movement and after that, they started to talk a little bit an then they told me everything, exactly what the staff said to my friend," said Mary Ellen Berger, French founder of the orphanage.
The Australian embassy in India has been informed about the misconduct of the 65-year-old doctor whose passport and visa for his stay in India have expired.
Officials also said that according to preliminary investigations, Allen had been arrested on similar charges a year back also.