The issue with the holes you have is not re-insulating them, but rather the vapour barrier. I cannot tell from the picture whether there was any there previously, but if it is the case , then just fibreglass or spray foam alone is not enough. You'll also have to restore the vapour barrier.
Usually, when fibreglass or spray foam insulation is used, there would be a layer of 6mil plastic right behind the drywall panel if you live in a predominantly heating climate. If your climate predominantly requires cooling, the barrier would be against the outside sheathing and thus a non-issue in your case.
If there was no vapour barrier, you can just stuff the hole with regular insulation, and cover with the existing cutouts or new pieces of drywall. No new barrier needed.
If a vapour barrier is required, then the simplest patch is to use closed cell expanding foam insulation (e.g. GreatStuff from dupont). Fill the hole with fibreglass or pieces of spray foam insulation until there is at most 3inches of space left.
Then fill the hole with an expanding closed cell foam suitable for the size of the gap, and let it expand, even it expands out of the cutouts. Ensure that enough goes behind the drywall so that it seals with the existing vapour barrier that is behind the drywall. Once cured, after about 15min, cut the excess off with a sharp utility knife, and cover.
Working with expanding foam is messy. Tape and cover off the work area, and wear gloves.