When I switched to Gmail more than a year ago, I still had a significant amount of old email stored with my old address. Because I keep messages for a long time and like to frequently search them, I wanted to move my old email to Gmail so it would all be in one place and I could access it on any device, including my mobile phone.
In the end, the move went smoothly, but I picked up a couple of tips along the way that I thought were worth sharing.
Setup
First, you need to tell Gmail how to retrieve your mail from old accounts using POP. Go to Settings > Accounts > Get mail from other accounts > Add another mail account. A new window will pop-up asking you for the email address you're going to import mail from. Fill this in and click on "Next Step."
I found it useful to label incoming messages with "Imported" (use any thoughtful label you can think of), so I could easily identify imported mail later on.
Then, validate with "Add Account" and finally, select "Yes, I want to be able to send mail as yourname@gmail.com." I'm a big fan of using the "from:me" search in Gmail that lets me look for email I sent using any name or address by simply searching "from:me." I wanted to make sure I could continue to find everything I’ve sent under all my old addresses and aliases, and this last step makes that work.
Sending mail from your old address
If you would still like to have the option of sending mail from Gmail that appears to recipients as if it were sent from your old email address, you can set up a custom "From:" by going to Settings > Accounts > Send mail as: > Add another email address.
Click on "Next Step" and then "Send Verification." You'll receive an email with instructions on how to validate your old address. Once it's set up, you can select this address in the "From" field when replying or forwarding.
It might take a while for Gmail to fetch everything from your old account, but the end result was definitely worth it for me.