Forward Mail from Gmail to Another Email Account Automatically

Gmail lets you automatically forward incoming mail to another address, if you’d like.

Here’s how to forward messages automatically:

Click the gear icon at the top of any Gmail page and choose Mail settings.
Click the Forwarding and POP/IMAP tab.
From the first drop-down menu in the “Forwarding” section, select ‘Add new email address.’
Enter the email address to which you’d like your messages forwarded.
For your security, we’ll send a verification to that email address.
Open your forwarding email account, and find the confirmation message from the Gmail team.
Click the verification link in that email.
Back in your Gmail account, select the ‘Forward a copy of incoming mail to…’ option and select your forwarding address from the drop-down menu.
Select the action you’d like your messages to take from the drop-down menu. You can choose to keep Gmail’s copy of the message in your inbox, or you can send it automatically to All Mail or Trash.
Click Save Changes.
You also can set up filters to forward messages that meet specific criteria. You can create 20 filters that forward to other addresses. You can maximize your filtered forwarding by combining filters that send to the same address.

How to stop auto-forwarding

If you no longer want to auto-forward your mail, follow these instructions:
Click the gear icon at the top of any Gmail page and choose Mail settings.
Click the Forwarding and POP/IMAP tab, or if you use Google Apps, you might have a Forwarding tab instead.
In the “Forwarding” section, select the Disable forwarding radio button.
Click the first drop-down menu in the “Forwarding” section and check for any forwards created by filtering. [source]