How do I record a loan paid off in QuickBooks?

You should have some sort of  Gain on Sale of Asset Acct or something similar that shows the full amount of the sale.  From that Acct you can transfer the Payment to the Long Term Liability Accounts to $0 out the loans.

There may be more involved though, so check with your Tax Accountant.  They may want/need to create a Journal Entry to show these payments, Closing Costs and multiple other Fees all related to making sure you only pay Income on the Income, not the Gross payment.

I should have added, but you probably already did, be sure to add a Memo that says something like the Final Loan Payments were sent by ABC Title Company at time of Sale. 

You may remember this, but it will make it easier for anyone else that looks at the books and for the Accountant to remember.  Especially if you switch Accountants in the near future and the new one it trying to figure out why the transaction did not go through the checking account.