Sara Kiran (29), Asif Malik (31), their daughter Zoha (7) and three sons Essa (4), Zakariya (2) and Yhaya (1), are in police custody in Ankara, a Turkish official told BBC.
The couple was arrested at a hotel in the Turkish capital after crossing into the country from Greece.
The family, from Slough in Berkshire, were reported missing on April 16.
Kiran's family had issued an emotional appeal for them to return to the UK earlier today.
"We are reaching out to Asif and Sara in the hope that they hear our messages, and we encourage them to make contact with us so we can return them safely to their families, who are extremely worried about them," said Thames Valley Police acting Deputy Chief Constable John Campbell.
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"It is an extremely dangerous place and not a place where young children should be taken," Campbell added.
Officers believe they travelled south through Europe, possibly by train, and passed through Budapest, Hungary, on or around April 12, he said.
The report comes as international intelligence officials revealed to The Sunday Times that at least 1,600 Britons have travelled to the Syrian and Iraqi battlefields, more than double the number previously reported.