Moving databases to other Storage

Hello,

We need more space for our databases, they're reaching 99% of our
capacity.

So we contracted a new Storage.

I've to move my DBs from the actual Storage to the new Storage.

How can i do this safely??

I think to make a full backup and restore it on the new Storage, but
im not sure if this is going to work.

Someone has any suggestion?!?

Thanks, and sorry my poor english