EXCLUSIVE

1:35 PM PT -- The store owners tell us Chris sent them a check on Monday for the full amount he owed them. And yes, this time they made sure the check cleared before informing prosecutors.

Chris Hansen ﻿is off the hook for allegedly bouncing checks -- which got him arrested in Connecticut -- because prosecutors dropped the charges ... TMZ has learned.

The former host of "To Catch a Predator" came up with the nearly $13,000 he owed to a mom-and-pop shop in Stamford, CT ... according to the court. As a result, prosecutors decided to drop the whole matter.

As we've reported ... Hansen was arrested and booked for larceny after allegedly bouncing 2 checks to the store owners.

Hansen’s attorney, Philip Russell, tells TMZ … Chris was in court Wednesday for a hearing, but he didn't have to plead to any charges after paying his debt in full.

As for when Hansen settled the tab, we'd assume he paid up after his arrest -- but when we posed that question to the court clerk we got a "no comment."