Combining Simple Products into One Product with Variations

I’m struggling a bit with variable products. I would like to know how to combine a bunch of existing products under one parent.

I know how to create a new parent product, and even change an existing product into a parent product, but it would appear that child products relating to the parent can only be created as new, and cannot be an existing SKU.

For example, I have a range of T-shirts, all the same except for size: S, M, L, XL.
They are currently set up as individual simple products – they were imported as such from Magento.

Ideally, I’d like there to be a parent product which allows customers to choose from the existing SKUs of different sizes.

Is that possible?