Barry was shocked when the 'Don't Look Back In Anger' songwriter made a beeline for him to reveal he's a big fan of his group the Bee Gees and the pair are going to go for an Indian meal in London.
The 'Night Fever' singer told The Daily Telegraph newspaper: "Noel Gallagher told me he always listened to my music. That to me is staggering. Because in the period when Oasis became big, we were gone. That was not our time.
"We're going to go for a curry. We can talk about what it was like being in a band with brothers."
The Bee Gees were comprised of Barry and his late younger siblings Maurice and Robin, while Noel was in Oasis with his younger brother Liam Gallagher before he quit the rock group following a huge bust-up between the pair in 2009.
Following their backstage hook-up at Glastonbury, Noel, 49, took to his Instagram account to upload a picture of him and Barry together and described their meeting as the "highlight" of his weekend at Michael Eavis' annual event at Worthy Farm in England.
He captioned the image: "Just got back from Glastonbury. This was THE highlight for me. One of my favourite songwriters of all time. BG and NG. (sic)"
Barry - who has sold more than 220 million records worldwide during his career - was thrilled to be asked by Chris Martin to join Coldplay on stage for their record-breaking fourth headline slot and he was touched that the crowd knew his two songs 'To Love Somebody' and 1977 disco classic 'Stayin' Alive'.
He said: "I was a nervous wreck ... but it was nice that people knew the songs."