You could do it a few different ways. A possibility to start with would be to just model half of it so you only have two corners to manage, if this is feasible.
The first thing to come to mind is to use edge loops to limit curvature. Place the edges and then use slide to get the curvature you want.
You could also Inset the box face, bevel the edge to the desired curve size and and then use edge loops to control the curvature.
Also, instead of Inset you could also Extrude, snap the face in position and then scale it to the desired size.
Here are some images to show both of those methods. Hopefully somebody has other ideas. You can never have to many ways of modeling.
This shows the box using edge loops at each corner. You can control the curvature by how close you put the new edge. Too close, though, and you can have problems.

The edge loop box subdivided

This box can be done with the inset tool and the Bevel the edges. However, you need to clean up the resulting Ngon by connection vertices or you won’t be able to use easily connection edges for your control of the corners.

The result after subdividing.
