For an animation I'd definitely use the spherise filter in photoshop as Nym said. I tried it to begin with but it didn't map the corners of the perimeter of the square to the perimeter of the circle (which is what I thought was wanted), so I went down the UV mapping route.

If want you want to do is an animation and are not too particular about the distortion, then go for spherise in stages saving each image as you go along and increasing the slider a notch, but note the image will still be square with a 'pushed out' sphere in the centre. You'd probably also have to do a warp too to make it move from a square to a circle in shape.

Isomage, when I was taking A level maths, I remember thinking what on earth I'd ever need those skills for in later life. Now I know, but I've forgotten it all!