Jackson and the Bee Gees singer are shown writing and recording a song titled 'All In Your Name' in the video, recorded by Gibb's daughter Ashley.
Gibb posted the video on his official website, saying: "Michael Jackson and I were the dearest of friends, that's simply what it was. We gravitated towards the same kind of music and we loved collaborating and he was the easiest person to write with.
"The more we got to know each other the more those ideas entwined and it all came to this song 'All In Your Name'. 'All in Your Name' is in fact the message that Michael wanted to send out to all of his fans all over the world that he did it all for them and for the pure love of music.
"I hope and pray that we all get to hear it in its entirety. This experience I will treasure forever."
Jackson's posthumous album of previously unreleased material, titled Michael, was released in December.
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Watch the short clip of Michael Jackson and Barry Gibb working together below: