He also told them he managed to tie his hands behind his legs and then "tied my legs to the boards of the bed".
Previously it had been revealed that black belt kickboxer Caroline had fought her husband for ten minutes before she died.
Babis spent more than a month claiming his wife was a victim of a gang of Albanian thieves who broke into the couple's home in Glyka Nera, near Athens.
The helicopter pilot has been described as a "top-class actor" by police as he was pretending to be devastated by his wife's death for 38 days.
Cops travelled to the island of Alonnisos where a memorial service for Caroline took place and asked him to follow them in order to give new testimony about the murder probe.
It is reported he told cops he "panicked" when he realised he had killed Caroline after holding her down in bed as the couple were having a late night row.
He also said he was considering hiding her body in a bid to mislead the police and claimed he did so because he didn't want his daughter to grow up without parents.
He even admitted killing the family's puppy in order to make the crime scene more plausible.
Meanwhile, heart-breaking entries of Caroline's diary revealed the couple's troubled relationship and that the young mum was planning to leave Babis for a long time.
The report reveals Caroline had several bruises on her body Credit: Social Media - Refer to Source The 33-year-old pilot confessed to killing his wife Credit: Athena Data showed that Caroline was asleep minutes before her death Credit: Social Media - Refer to Source
HOW YOU CAN GET HELP: Women's Aid has this advice for victims and their families:
Always keep your phone nearby. Get in touch with charities for help, including the Women’s Aid live chat helpline and services such as SupportLine. If you are in danger, call 999. Familiarise yourself with the Silent Solution, reporting abuse without speaking down the phone, instead dialing “55”. Always keep some money on you, including change for a pay phone or bus fare. If you suspect your partner is about to attack you, try to go to a lower-risk area of the house – for example, where there is a way out and access to a telephone. Avoid the kitchen and garage, where there are likely to be knives or other weapons. Avoid rooms where you might become trapped, such as the bathroom, or where you might be shut into a cupboard or other small space. If you are a victim of domestic abuse, SupportLine is open Tuesday, Wednesday and Thursday from 6pm to 8pm on 01708 765200. The charity’s email support service is open weekdays and weekends during the crisis – messageinfo@supportline.org.uk .
Women’s Aid provides a . from 10am to noon.
You can also call the freephone 24-hour National Domestic Abuse Helpline on 0808 2000 247.
Killer husband of Caroline Crouch says he ‘deserves his punishment’ after telling cops he suffocated Brit mum because he ‘lost his temper'