How soon can you transfer iTunes accounts?

You can logout of the currently logged in account by tapping on your id in Settings > iTunes & App Stores and you can then log in with a different account (you can't transfer content from one account to another account). But if you turn on automatic downloads for an account, use iTunes match or re-download its past purchases then you risk tying your iPhone (and the same principle applies to computers) to that account for 90 days : http://support.apple.com/kb/HT4627

If you want past purchases from an account, then do you have all of your content from both accounts on your computer's iTunes so that you can sync them over ?

It depends upon what you do with the account. If you use automatic downloads, iTunes match, or re-download purchases and the 90 day counter starts then yes, you will need to wait until the 90 days has completed - if you don't do those or if the 90 days counter doesn't start then you can log out and in immediately.