The Bee Gees singer died yesterday (May 20) after a long battle with colon and liver cancer.
The legendary pop group provided the soundtrack to the iconic Saturday Night Fever starring Travolta in 1977, which helped bring disco music to even bigger heights. It also helped launch the career of the Grease actor.
"I thought Robin was one of the most wonderful people," Travolta told TMZ.
"Gifted, generous, and a real friend to everyone he knew. And we'll miss him."
The songwriter's death has seen an outpouring of grief and tributes from the showbiz and music world, including messages from the likes of Bryan Adams, Liam Gallagher and Justin Timberlake.
Robin Gibb had said in 2010 that he had never actually watched Saturday Night Fever, despite his hugely successful soundtrack.
The Saturday Night Fever soundtrack has sold over 15 million copies in the US alone, and stayed on top of the UK album chart for 18 weeks.
It included the tracks 'Stayin' Alive', 'Night Fever', 'How Deep is Your Love', 'Jive Talkin'', 'More Than a Woman' and 'You Should Be Dancing' among others.
Watch the trailer for Saturday Night Fever below: