Option 1: Using an old phone and new phone number to access WhatsApp messages on the old phone. You just need to change the number linked with WhatsApp from the old number to the new one.
This can be done within WhatsApp. Go to Menu Button > Settings > Account > Change number.
Option 2. Using a new phone and a new phone number, and transfer WhatsApp message to new phone. You'll still have to change phone number like option 1. Then transfer chat history from old phone to new phone. If your WhatsApp messages are backed up to Google Drive, you can just install WhatsApp on your new phone after changing phone number and the app will find the backup on Google Drive.
You can find the official answer from WhatsApp FAQ.