Yes.
Downloading previously purchased & downloaded apps
When you download a paid or free app on Google Play, the app is connected to your Google Account, meaning that you get several benefits:
If you get a new device, remove an app to free up space, or reset your device, you can reinstall the app without purchasing it again.
If you have multiple devices, you can install the app on all of your devices without purchasing the app again.
You can quickly find free or paid apps that you previously downloaded.