How can I close and seal an abandoned downspout opening?
I have covered over holes similar to this using thin aluminum sheet (and copper on copper gutters) bent to shape to fit the inside of the gutter and then pop riveted in place (after applying a little low modulus silicone sealant around the hole on the inside and along the outer edges of the repair section to stop water going in between. 

It does of course squeeze out some sealant during the riveting process so you might need to use a paintable sealant if you're painting the guttering outside. The ones I've done have not been visible from the ground, luckily enough. 

It's also possible to put the repair sheet on the outside of the guttering if you're careful, which may look neater to the eye.