First log into your account with your existing email address.
Then mouse over your email address in navigation bar on the top right, and click 'Edit my password', or if you're already logged in now, click here to open this page in a new window.
Now enter your new email address in the 'Email' field, and your current password in the 'Current password' field, and click the 'Update' button. You can leave the other two fields blank.
You'll then receive an email to your new email address, this will ask you to click a link to confirm the change of email. Once you click this you'll be able to sign in with your new email and existing password.