The short answer is that you can do this by making the blog in question a team blog, with two members, then removing the original team member.
In detail, the process goes like this:
- Sign in to Blogger with Account 1, which we'll assume is the account containing the blog.
- Go to the "Permissions" section under Settings | Basic tab.
- Click the Add Authors button and send an invitation to the owner of Account 2, the account to which you'd like to move the blog.
- Wait for the owner of Account 2 to accept the invitation. If you're sharing a computer, you'll need to sign out of Account 1 first, or each use a different browser.
- Once Account 2 has joined the blog, Account 1 can sign in again and go back to the Settings | Basic tab.
- Click the drop-down menu next to Account 2 and choose "Admin."
- Click the X next to Account 1 to remove Account 1.
- You'll still see any posts made on the blog by Account 1 with Account 1's display name. Account 2 can delete and repost these posts if they'd like to change the display name.
- Account 1 cannot be removed until Account 2 has admin rights, since every blog must have at least one admin member at all times.
- Photos uploaded with Account 1 will break if that account is deleted. If you want your old photos to display after adding Account 2, you'll have to leave Account 1 active.