WhatsApp updated their Windows Phone beta app, allowing data and texts from the app, to be safely stored on Microsoft's cloud service, OneDrive. (Via Windows Central).
To enable this new feature, simply make sure you have the beta version of the app installed, then head over to Settings > Chat and Security > Backup. From there, you can adjust if you want the backup to be manual or automatic. If you choose automatic you have a few options like daily, weekly and monthly. There is also a useful feature that disables the backup on cellular data and only allows it to work on Wi-Fi, which is great for people with the limited data plans.
As WhatsApp Beta is a pre-release version of the original WhatsApp, we should expect the feature to come to regular "stable" users at some point.