Step 1: Register for an Outlook.com account.
Skip this step if you already have a Microsoft account or Hotmail address that you’d like to use.
Step 2: Tell Gmail to forward your mail to Outlook as it arrives.
Log in to your Gmail account, and click Settings. Then choose the Forwarding/POP/IMAP tab, and choose to Forward a copy of incoming mail to your new Outlook.com account. Then scroll to the bottom of the page, click Save Changes, and click the verification link in the email you receive. Your Outlook.com account will automatically sync with your Gmail account to retrieve your email in that account.
Step 3: Link your Gmail contacts to Outlook.com.
This step is optional, but it will help make sure you have all your contacts automatically at your fingertips in your new Outlook.com account. That way, when you create a new email, you'll have your entire address book available.
Step 4: Choose to send from either your @Outlook.com or @Gmail.com address.
If you'd like to still use your Gmail address, add that address as a send-only account. Then, you’ll be able to send from either your new, @Outlook.com, or your current @gmail.com address.
Click Options, More mail settings, then click Your email accounts, and choose Add a send-only account. Outlook.com will send a verification email to your Gmail address to make sure you have the right to send email from it.