You need to have a professional licensed asbestos remediation company come remove the asbestos containing popcorn. They usually set up containment, air exchange, etc, and scrape the popcorn texture off. You will then have to have the ceiling skimmed or textured before paint.

I had a home with ceiling tiles over plaster that I wanted to remove. They did, only to reveal black lumpy glue that had been used to adhere the tiles to the ceiling. We installed the thinnest drywall over the ceiling, and you cannot tell that it is anything but a plaster ceiling. While Beth H.’s solution is more decorative (and attractive!), this is probably your least expensive solution. Good luck! (And…stay out of the attic!)

You can have drywall basically glued to the current ceiling...

It's accepted environmental practice to leave it in place and cover it over with another material, like a new layer of sheetrock, rather than disturb it by removing it. However, you will want a company that is experienced in this as otherwise you could end up with a bigger mess on your hands. Also, even if you remediate by safely covering it, you will still be legally required to list the presence of asbestos in the disclosures when you go to sell the house.

YIKES you have a problem!! Asbestos abatement is very expensive. I think you need to abandon 'opinions' and head to the experts/ professionals.

Since asbestos is only a problem when airborn and you already have a big hole taking down all the sheetrock without scraping would be safest. I don't know how much abatement by pros would cost but the cover up problem is not ver appealing. Its just kicking the can down the road and when its time to sell your house at disclosure you can say its gone instead of its concealed underneath a layer of something else.

IMO asbestos abatement is the biggest rip off and you do not need it . the ceiling can be covered and IMO you need to put some type of flooring in the attic too Those ceilings can be removed by you with a ton of water huge plast bags and plastin on the floor but when you go to the dump it will cost you a lot. Cover it with the thin ceiling panesl it will be nice looking and no chance of the asbestos dust flying around. If it is encapsulated it is not threat to anyone.Hosestly it would take years of being exposed to the dust to affect your health.

Simply cover it with 5/8" drywall screwed to the joists. This isn't difficult or expensive.

No need to cover with wood or remove the existing. Just cover it.

I used to work as an environmental engineer/regulator in the area of management of toxic substances, including asbestos. There's a reason professional abatement by certified asbestos specialists is expensive: to do it right takes training, proper protective equipment, temporarily closing off the room and all duct work to it, negative pressure air machines, HEPA vacuums, followup testing, and disposal of the debris at a dump authorized to accept hazardous waste. Carefully consider whether you can do this yourself and not make a mess that contaminates your house. I've taken too many calls from people who regretted this halfway through the project, or worried later about whether they had created a health risk for their families. That's why your best option is probably to have it covered in place. But if you think you're up for removing it yourself, check with your local/State pollution control agency, or a regional office of the federal EPA for written procedures. If you use a company, these organizations will also have a list of authorized/licensed remediation companies.

Thank you to everyone for answering! It seems like the best option is to just cover it up for now. My plan is to use something like drywall or panels, but would you recommend fixing the hole first before doing that? Or can I just cover up the hole as we are putting up the drywall? We have an HVAC unit up in the attic, so if I leave the hole there, would the warm air affect the new layer of drywall? I know the popcorn ceiling leaves little air gaps because of the texture, so I'm wondering if that would affect the new drywall installation if I just left the hole in place.

Leaving the hole alone and installing sheetrock is all you need to do. When you sheetrock, part of the process is to tape/mud all seams and exposed edges. Once that is done, you won't be getting any air flow in or out of the hole. And even if you did, it would have no effect on the new sheetrock. My vote is to not cause yourself additional work and potential problems by messing around with this damaged material. I also suggest you rent and use a drywall lift when getting the sheetrock panels in place. It will make the job faster and easier, it will prevent you from injuring your back or doing damage to the walls, and it will minimize the likelihood of releasing more asbestos as you are trying to get the panels in place.

Drywall lift video