The man and his wife entered a surrogacy arrangement with a Thai woman several years ago, the ABC reported on Monday.
The Thai mother was told of the abuse allegations in June 2013.
The man has been charged with indecent dealings of a sexual nature with the children while they were under 10.
He has also been charged with possessing child abuse material but denies all the allegations, the ABC says.
He faces court later this year.
After the couple returned to Australia with the twins, their marriage broke down.
The children are now being cared for by the man's ex-wife and Australian child welfare authorities are considering plans for long-term care, the ABC reported.
Surrogacy arrangements in Thailand have come under scrutiny recently because of the case of baby Gammy, a surrogate-born boy with Down syndrome whose Australian parents left him behind.
The Thai government is considering new legislation to ban the practice.
Thailand and Australia are working out a transition process for an expected 150 Australian couples and Thai surrogate mothers expected to give birth over the next year.
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