Alanis Morissette -- You Oughta Know ... I GOT MY DOG BACK!!!

The Alanis Morissette dognapping saga is OVER ... TMZ has learned the rocker's prized pup has been returned to her.

As TMZ first reported, Morissette sued her old housekeeper claiming the woman stole her dog -- a 10 lb Chihuahua/Pug mix named Circus -- after Alanis fired her.

The housekeeper claimed Alanis hated the dog and wanted her gone.

But isn't it ironic ... today in court, Alanis' attorney dropped the suit because Circus is now safe and sound back at the home of Alanis and her hubby, Mario Treadway.

It figures.