Firstly, you will need to back up your messages in the previous phone.
To back up, follow these steps: Go to WhatsApp > Menu Button > Settings > Chat settings > Chat Backup. These will be saved in a the WhatsApp folder in your file manager.
You are set, next, transfer this backup to your new Android phone. If your phone has an external microSD card, take the microSD card out of your old phone, and pop it into your new one. If your phone does not have a memory card but comes with an internal memory alone, you can transfer the folder to your new phone using your computer or an application like file explorer.
When installing WhatsApp on your new phone, it will automatically find your backup and ask you if you would like to restore it.
Once restored, your old chats will appear on your new phone, have fun chatting on whatsapp.