Barry will take to the stage on the same night that the first pair of dancers will leave the competition.
The BBC tweeted: "SUNDAY NIGHT FEVER @GibbBarry will perform on the first #Strictly results show! 2nd October @BBCOne."
Barry Gibb will perform on the first results night
Barry, 70, will release his first solo album titled In The Know just five days after his Strictly performance. Over the summer the legendary Bee Gee wowed fans at Glastonbury, performing with Coldplay.
The How Deep Is Your Love singer is the only surviving member of the pop group. Barry's twin Robin passed away in 2012; his younger brother Maurice died in 2003 at the age of 53.
The 15 Strictly Come Dancing hopefuls
This year's 15 contestants and their dance partners are currently locked away in the dance studio rehearsing their group dances and individual dances. The couples were revealed on the show earlier this month, but the next episode doesn't air until Friday 23 September.
HELLO! Online caught up with Strictly contestant Melvin Odoom, who is hoping to raise the glitterball trophy this year. The radio presenter has been paired with Janette Manrara for the competition.
The show's first live episode will return on Friday 23 September
"I think she's the best partner that I could have got to be honest," said Melvin. "Because she's the perfect balance of being able to take things seriously, but she's very fun at the same time."
He added: "She does work me quite hard but she's really worked me out, she's taken some time to get to know me."
Melvin admitted that ahead of the competition, he has turned to former contestants including Pixie Lott and Caroline Flack for advice.
"Pixie I saw at V Festival, who's a really good friend of ours, she was amazing," he revealed. "She said, 'Melvin, really enjoy it because it's over sooner than you think and at the end of it you realise how great it is'. Caroline was really amazing as well, she said it was one of the best things she's ever done."