The singer released the clip - which sees her stripping to her underwear in a hotel room - as a thank you to fans ahead of the final show on her 'Black Star' tour.
She said: "I decided to shoot a little video for my song 'Goodbye'... at the Chateau Marmont in Los Angeles.
"I just wanted this to be something to give to you guys to say thank you and to complete this album cycle."
The song is taken from her latest record Goodbye Lullaby, which peaked at number four on the Billboard chart and at nine in the UK, shifting 1.3 million copies to date.
It was recently reported that the star is in the running to judge The X Factor USA.
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Watch the 'Goodbye' music video below: