Dropbox
Drop-in replacementFree with paid extrasThe official Linux app. Same account, same folder, same behaviour as Windows.
Your files: Your existing files sync down unchanged.
Does Dropbox run on Linux?
Verdict: Yes
Yes. Dropbox makes an official Linux desktop app, supported on Ubuntu 18.04 or later and Fedora 28 or later, and it gives you the same syncing folder you have on Windows.
Dropbox's help centre describes the Linux desktop app and names Ubuntu 64-bit 18.04 or later and Fedora 64-bit 28 or later as officially supported. It adds that other Linux systems are not officially supported but may work if they meet the requirements, which in practice covers Linux Mint, Zorin and Pop!_OS since those are built on Ubuntu.
Once installed you get the familiar Dropbox folder in your file manager, files syncing in the background, and the small icon near the clock showing progress. Sharing links, version history and selective sync all work.
Two things to know. The tray icon needs a desktop that supports the AppIndicator system, which covers KDE Plasma, Xfce, MATE and GNOME with a small extension that most systems install for you. And Dropbox is fussy about the type of drive its folder sits on, so keep it on your main drive rather than an unusual or encrypted partition.
Your files are in Dropbox's storage, so nothing is at risk. Install the app on Linux, sign in, and the same folder rebuilds itself. On a slow connection this takes a while, so use selective sync to choose what comes down first.
Dropbox on Linux, and alternatives
Nextcloud
Close matchFree with paid extrasWorth considering if you would rather host your own storage or pay a smaller provider. Same idea of a syncing folder.
Your files: You upload once. Files are stored plainly and open normally.
Syncthing
Different way of workingFreeFree and keeps folders matched directly between your own devices with no cloud account. No website copy of your files.
Your files: Copies files between machines unchanged.
Déjà Dup Backups
Different way of workingFreeNot a sync tool. Use it alongside Dropbox so you have a real backup rather than just a mirrored folder.
Your files: Stores encrypted backups of any folder you choose.
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