The 'Candy' singer recruited modern-day crooner Michael to appear on the sequel to his 2011 album 'Swing When You're Winning', which he is currently recording.
Michael told the Daily Star newspaper: ''I got to know Robbie through [TV show] 'The X Factor' and I love him.
''The song is for his new swing album and it's so good. We had too much fun making it.''
The pair also share something else musical in common, as they have both recorded versions of the track 'Somethin' Stupid' with actresses. Robbie recorded a at version with Nicole Kidman for 'Swing When You're Winning', while Michael teamed up with Reese Witherspoon for his take on the track for his new album 'To Be Loved'.
Despite Robbie coming from a boy band, Take That, and seen as more of a pop artist, Michael sees similarities in their characters.
He added: ''Robbie has probably been more open than I have with certain things. I'm pretty open but he's bared his demons.
''I have the same demons, so we talk about all the things I think about as I don't have other people to talk to them about. It's pretty awesome.
''I have truly enjoyed my conversations with Robbie.
''Both of us were dealing with the insecurity, both of us were dealing with everything about the way we could live, both of us probably do what we do too much.''
'To Be Loved' is released on April 15.