The 39-year-old singer and the 28-year-old pop star have teamed up for a version of classic song 'Dream a Little Dream of Me', which has been recorded over 60 times by artists such as Ella Fitzgerald, The Mamas & The Papas, Doris Day and Dean Martin.
Although Lily was thrilled when Robbie asked her to join him on the track she confesses she was a bit nervous when she got in the studio with him.
She said: '''Dream A Little Dream' is one of my favourite songs of all time so I didn't hesitate when Robbie asked me if I'd like to duet with him on it. I was a bit nervous when we recorded it, especially when I asked him what he wanted me to do and he said something like 'just be you'. But I'm really happy with it and think we do justice to a classic song.''
Robbie and Michael sing together on 'Soda Pop' and the Canadian crooner believes fans will enjoy the fun track.
Michael said: ''The song is for his new album and it's so good. We had too much fun making it.''
As well as a number of swing classics, the LP - which will be released on November 18 - also contains six original songs with Robbie co-wrote with songwriting genius Guy Chambers.
It is Robbie's first big band album since 2001's 'Swing When You're Winning'.
'Swings Both Ways' full tracklisting:
'Shine My Shoes'
'I Wanna Be Like You' - featuring Olly Murs
'Swings Both Ways' - featuring Rufus Wainwright
'Dream A Little Dream of Me' - featuring Lily Allen
'Soda Pop' - featuring Michael Buble
'Puttin' On The Ritz'
'Little Green Apples' - featuring Kelly Clarkson
'Minnie The Moocher'
'If I Only Had A Brain'
'No One Likes A Fat Pop Star'
American Thighs was released on this day in 1994.