Minogue can be seen chewing on Daley's tie in the picture which he shared with his followers on Twitter, accompanied by the caption: "@kylieminogue and I :)"
The Olympic medal-winning diver also posed with One Direction's Niall Horan and Louis Tomlinson, adding: "Yes...they are wearing the same suits!!! Haha @niallofficial @louis_tomlinson."
The 18-year-old sports star then added a photo of himself with Natalie Imbruglia, who also attended the party at Babington House in Somerset.
Other star guests included Doctor Who's Matt Smith, Michael McIntyre, Jimmy Carr, David Walliams and best man Ben Winston, the son of fertility expert Professor Robert Winston.
X Factor host Dermot O'Leary tied the knot the day before (September 14) at St Mary's Church in Kent.