The 'Troublemaker' hitmaker has revealed he got himself into the spirit of the pair's famous 2000 hit from the Australian pop princess' LP 'Light Years' by pretending to be her, before going on stage to perform the song with Robbie when he supported him on the 'Take the Crown Stadium Tour' in 2013.
Olly recalled: ''He invited me to sing 'Kids' with him every night in his set - and I dressed up as Kylie backstage as a joke for him.''
The 35-year-old pop star - who shot to fame on 'The X Factor' in 2009 and performed 'Angels' with Robbie on one episode - also supported boyband One Direction on their first International 'Up All Night Tour' - which took place between 2011 and 2012 - on select dates in the US, and says it the opportunity awarded him the chance to build his own audience across the pond.
Speaking about the ''crazy'' experience early on in his career, the entertainer told The Sun newspaper's Bizarre column: ''I supported One Direction on their 'Up All Night Tour' when they blew up in America. It was a crazy experience. It was like touring with The Beatles.
''Fans ran after the cars, crowds waited outside the hotels in their hundreds. To support them there gave me a real leg-up in America and helped me to launch my music there.''
The 'Dance With Me Tonight' hitmaker went on to co-present 'The X Factor' with Caroline Flack in 2015, before landing a spot as a coach on 'The Voice' in 2018.
Olly recently revealed he wants to work with both this year's winner of the latter show, Molly Hocking, and his finalist Jimmy Balito.
Speaking exclusively to BANG Showbiz, he said: ''What they decide to do after the show is up to them and their path but I'm always going to be there for them like I was with the other contestants last year. So if they ever want to work together, write a song, I'm always here.''