The three stars have donated their time to perform for Caudwell Children's Butterfly Benefit fundraising event, which is set to take place on May 12 at the Banqueting House in Whitehall, London.
Robbie, who is an official ambassador for the children's charity, has agreed to perform for the 250 invited guests.
Trudi Beswick, chief executive of Caudwell Children, added: 'We are honoured to have Robbie as an ambassador for the charity and delighted that we have this opportunity for him to perform for us alongside Gary Barlow and Robin Gibb.'
Caudwell Children has currently provided more than £13 million of support to children with over 350 different medical conditions.