If you prefer open source tools you can run yourself then rclone will do exactly this.
(rclone author)
(rclone author)
We can assure you that MoveBot is built on its own and does not use Rclone in anyway.
You can also expose rclone synced cloud storage folders over FTP/HTTP. For instance https://docs.dapt.in/ is a rclone synced gdrive folder exposed running on daptin :)
(daptin author)