This worked for me:

• Rename the file ~/Library/Keychains/login.keychain (to keep it safe just in case)
• Drag your backup copy of login.keychain to the same location
• Make sure your admin account on your new system (or install of OS X) has the same password as the old one, or (according to JTJ) it won’t automatically open it when you log in.

Source: Originally tweeted.