Anderson, 31, has spoken to nearly all his fellow housemates about his switch from being a female to a male on the Channel 5 reality show.
Bill and Christine Anderson have told the Daily Star that they never had any issues with Luke's decision to have surgery and switch genders.
"I had lost a daughter - and a gorgeous-looking girl at that. But I had also gained another son and we both knew at last he was happy," said Bill.
"When you are a parent anything your child does, you love them unconditionally. You want the best for them and you carry that through."
Luke is not the first transgender Big Brother housemate. Nadia Almada, who went on to win the fifth series on Channel 4, was born a boy.
