Maurice, who died in 2003 aged 53, composed Jive Talkin’ on the J45 after driving across a bridge in Florida and hearing the rhythm made by the car’s tyres on the road surface.
It was the first single from the Bee Gee’s 1975 album Main Course – and marked a turning point in the three-piece’s career as they moved from ballad to disco.
The hit reached No1 on the US Billboard Hot 100 – and was regarded as the Bee Gees’ comeback after a lull in popularity in the early 70s.
Jive Talkin’ caught the ear of film directors who asked them to contribute six songs to 1977 film Saturday Night Fever.
Stayin’ Alive, How Deep Is Your Love and Night Fever are the first songs on a soundtrack which propelled the Bee Gees into global chart dominance.
The EBS-1250 combines a bass and guitar into a single instrument – and was sold by Maurice in 1974 to a collector who has owned it since.
It is believed to be the only one of its kind made by Gibson in the year of 1968.
The instruments will be sold at Gardiner Houlgate in Corsham, Wilts., at the UK’s largest guitar auction.
The Bee Gees was made up of brothers Maurice, Barry and Robin Gibb.
In 1987 Maurice donated the J45 to Radio 1 to give away as a prize on The Bruno Brookes show.
It was autographed by all three Gibb brothers.
The prize winner sold the guitar on Channel 4 auction show Four Rooms in 2014.
Luke Hobbs, Gardiner Houlgate auctioneer, said: “Bee Gees’ instruments are exceptionally rare and neither of these guitars has ever been offered for public auction before.
“We have great provenance on both. The J45 is well documented as the guitar on which Maurice Gibb composed Jive Talkin’. We’ve also got the letter from Radio 1 to the gentleman who won it.
“Maurice was photographed performing with the double-neck and he can be seen playing it on stage in a video on YouTube.
“These guitars represent the two great phases of the Bee Gees’ career.
“The double-neck comes from the 60s and early 70s when they sang popular ballads – the J45 represents their comeback and the disco years.
“It’s not often you get to encapsulate a band’s career so succinctly in a single auction.
“We’ve over 400 guitars in September’s sale, making this the largest ever auction of guitars held in the UK, possibly the world. We’re expecting massive international interest.”
The Maton guitar used by George Harrison at the Beatles’ last appearance at Liverpool’s Cavern Club in 1963 will also be auctioned in this sale.