It will be a two step process - download all your photos, videos, music, and docs from Verizon cloud (in chunks, or groups of a few hundred at a time. otherwise the process chokes and files get corrupted, it seems) as ZIP files.
Then you'll need to unzip the files,a nd re-upload them to your Google drive. If any of the items are still on your phone you can back them up to Google and save the extra step of downloading from Verizon. Then set your phone to back everything up to Google instead of Verizon.