The "19 Kids and Counting" star has pled guilty to a third-degree count of endangering the welfare of a minor in Arkansas -- this according to court docs obtained by TMZ. The paperwork shows Jana entered her plea on Dec. 15 ... closing the book on her case.

As a result, she had to pay fines and fees -- totaling $880 ... with $100 of that going toward what the court describes as a Child Victim Crime Fee.

Jana, who'd initially pled not guilty, explained what this was all about last month -- when news about her criminal case broke. She said she was babysitting, and one of the kids slipped out through the front door unnoticed by accident.

Somebody saw the child outside and called cops, which resulted in Jana getting ticketed. She said it was a mistake that could've happened to anybody ... and denied doing anything to purposely put any of the children at risk. Her family backed her up in supporting statements.

The timing of her charge coincided with her brother, Josh Duggar, getting convicted in his child porn case ... which made some folks believe she herself might've been wrapped up in something more dubious than just a babysitting slip-up.